The name Mahalakshmi could either refer to the Consort of Lord Vishnu, or to Lalita Tripura Sundari, or to MahisaMardini Durga (Chandika), or to Matrika Devi, or to some specific form of Devi also.
Mahalakshmi as the consort of Lord Vishnu:
Consort of Lord Vishnu who always resides with Lord Vishnu is also known by the name Mahalakshmi. For example Padma Purana describes her as:
गृहीतशंखचक्राभ्यामुद्बाहुभ्यां विराजितः ३८।
वरदाभयहस्ताभ्यामितराभ्यां तथैव च ।
वामाङ्के संस्थिता देवी महालक्ष्मीर्महेश्वरी ३९।
हिरण्यवर्णा हरिणी सुवर्णरजतस्रजा ।
सर्वलक्षणसंपन्ना यौवनारंभविग्रहा ४०। (Padma Purana)
He shines with his raised arms that have held the conch and the disc. So also (he shines) with the other two hands granting boons. On his left thigh is seated goddess Mahalakshmi, the great deity. She has a golden complexion and is deer-eyed. She has (put on) a wreath of gold and silver. She is endowed with all (auspicious) marks and her body has (just) the commencement of youth.
Her form is described as:
तप्तकांचनवर्णाभा तप्तकांचनभूषणा ।
हस्तैश्चतुर्भिः संयुक्ता कनकांबुजभूषिता ४४।
नानाविचित्ररत्नाढ्या कनकांबुजमालया ।
हारकेयूरकटकैरंगुलीयैश्च शोभिता ४५।
भुजद्वयघृतोदग्र पद्मयुग्मोपशोभिता ।
गृहीतमातुलुंगाख्य जांबूनदकराञ्चिता ४६।
Her complexion resembles gold purified with fire. Her ornaments are made of gold purified by fire. She is endowed with four hands. She is adorned with a golden lotus. She is abounding in various beautiful gems. She is also adorned with necklaces, armlets, bracelets and rings. She shines with a couple of big lotuses held in both her hands. Her hands are graced with golden ornaments called citrons.
Nagara Khanda of Skanda Purana gives a story of how Lakshmi devi (consort of Lord Vishnu) once got a curse and became elephant-headed. To get her original face back again she does tapa of Lord Brahma, and Lord Brahma tells her from now you will be known by the name Mahalakshmi.
Lakṣmī said:
For some reason, O Lord, I have been transformed into an elephant-faced woman by an extremely furious Brāhmaṇa by uttering a terrible curse. Hence, O Pitāmaha, if you are pleased, change me back again into the old form. I do not choose anything else.
Brahmā said:
O fair lady, with my favor, your face will undoubtedly become splendid all the more. So go home. O splendid lady, Mahattva (greatness) has been granted to you by me from today. Hence your name here will be Mahalakshmi. A man who devoutly worships you as elephant-faced, shall become a king on the earth and Lord of elephants. On the second lunar day, O goddess, one who calls you Mahalakshmi and devoutly worships you through Śrīsūkta will never become poor during seven successive births. (Skandha Purana)
Thus from above it is proved that Lord Vishnu's consort is also known by the name Mahalakshmi and she is also worshipped by the name Mahalakshmi.
Mahalakshmi as Lalita Tripurasundari:
Mahatripurasundari is known by the name Mahalakshmi.
Lord Hayagriva tells in the Brahmanda Purana:
मन्त्रं श्रीचक्रगेवास्याः सेयं हि त्रिपुरांबिका । सैषैव हि महालक्ष्मीः स्फुरच्चैवात्मनः पुरा ॥ ३,४१.३ ॥ पस्यति स्म तदा चक्रं ज्योतिर्मयविजृंभितम् । अस्य चक्रस्य माहात्म्यमपरिज्ञेयमेव हि ॥ ३,४१.४ ॥ साक्षात्सैव महालक्ष्मीः श्रीचक्रमिति तत्त्वतः । यदभ्यर्च्य महाविष्णुः सर्वलोकविमोहनम् । कामसंमोहिनीरूपं भेजे राजीवलोचनः ॥ ३,४१.५ ॥ अर्चयित्वा तदीशानः सर्वविद्येश्वरोऽभवत् । तदाराध्य विशेषेण ब्रह्मा ब्रह्माण्डसूरभूत् । मुनीनां मोहनश्चासीत्स्मरो यद्वरिवस्यया ॥ ३,४१.६ ॥ (Brahmanda Purana)
Hayagrīva said.:
3-6. Sri Chakra alone is her Mantra (Yantra). She is Tripurāmbikā and she is Mahalakshmi herself. Formerly, the Cakra was seen coming out of Ātman throbbing and sparkling. It expanded and increased in luminosity. Indeed the greatness of this wheel (circle) cannot be (fully) comprehended. The fact is Srichakra is Mahalakshmi herself. It was by worshipping it that the lotus-eyed Mahāviṣṇu attained the form of Kāmasammohinī (Enchantress of even god of Love), fascinating the worlds. After worshipping it, Īśāna became the lord of all lores. By propitiating it particularly Brahmā became the progenitor of the Cosmic Egg. It is by means of its worship that the God of Love became the enchanter of even the sages.
Thus from above it is clear that Sri Yantra which is identical to Lalita Tripurasundari is identified as Mahalakshmi herself. For the worship of Sri Yantra, the chapter continues:
He should propitiate Mahalakshmi by means of splendid food offering such as honey, ghee, sugar, milk puddings and other blameless articles as well as black gram cakes of pleasing nature. The intelligent devotee should thus propitiate Mahalakshmi in three Maṇḍalas. Parameśvarī immediately appears before him.
And further it is told:
कामाक्ष्यैव महालक्ष्मीश्चक्रं श्रीचक्रमेव हि । श्रीविद्यैषा परा विद्या नायिका गुरुनायिका ॥ ३,४१.१५ ॥
Kamakshi alone is Mahalakshmi. The Cakra is Śrīcakra itself. This Śrīvidyā is the greatest Vidyā (i.e. Mantra).
In the Brahmanda Purana, Lord Hayagriva further explains to Rishi Agastya in another chapter also as:
Agastya said:
What are the different sportive and gracious activities of Mahātripurasundarī who is installed on the pedestal of Kāmakoṣṭha and who is well-renowned as Kāmākṣī? That goddess Mahātripura-sundarī who is Maheśvarī herself is well known as Śrīkāmākṣī. She is stationed in the terrestrial sphere. What are the activities of this goddess? O most eloquent one, recount to me her divine life.”
Hayagrīva said:
“Although she is stationed here (on the earth) O Pot-born Sage, she abides in the heart of everyone. She bestows the fruit of acts on all embodied beings in accordance with their different activities. Whatever happens in the world is the result of her activities. One may think something, but she disposes of it freely in accordance with her will. The Śaktis beginning with Tripurā are her own incarnations. She herself was Mahalakshmi. She created three eggs formerly. Those eggs were the abode of the three great Devas as well as the three Śaktis. From one egg were born Ambikā and Puruṣottama; from another egg were born Śrī (goddess of wealth) and Viriñca (Brahmā) and from the other, the third, were born the goddess of speech and Śiva. Maheśvarī united (in marriage) Indirā (the goddess of wealth) with Mukunda (Puruṣottama). She joined Parameśāna with Pārvatī and Pitāmaha with Sarasvatī.
Thus, from above it is clear that Lalita Tripurasundari herself is worshipped by the name Mahalakshmi. Sri Yantra itself is called as Mahalakshmi.
Mahalakshmi as Durga Parameswari:
Mahisasura-Mardini form of Durga is also called by the name Mahalakshmi. Durga Saptashati also known as Sri Chandi is divided into three parts Prathma Charitra, Madhyama Charitra, and Uttama Charitra. In the prathama charitra destruction of Madhu Kaitabha is described. In the Madhyama Charitra destruction of Mahisasura (and his army/generals) is described. In the Uttama charitra destruction of Sumbha Nisumbha (and his army/generals). Prathama Charitra is presided over by Mahakali, Madhyama Charitra is presided over by Mahalakshmi and Uttama Charitra is presided over by deity Mahasaraswati.
Here Mahalakshmi is Durga herself who manifests from inner Shakti of all gods to kill Mahisasura. Various deities provide her with various weapons. Himavan provides her Simha (the lion), her vehicle.
Shiva Purana in the chapter, Incarnation of Mahalakshmi clearly describes it as:
इति देववचः श्रुत्वा दामोदरसतीश्वरौ ।।
चक्रतुः परमं कोपं रोषाघूर्णितलोचनौ ।। 5.46.१० ।।
ततोतिकोपपूर्णस्य विष्णोश्शंभोश्च वक्त्रतः ।।
तथान्येषां च देवानां शरीरान्निर्गतं महः ।। ११ ।।
अतीव महसः पुंजं ज्वलन्तं दशदिक्षु च ।।
अपश्यंस्त्रिदशास्सर्वे दुर्गा ध्यानपरायणाः ।। १२ ।।
सर्वदेवशरीरोत्थं तेजस्तदतिभीषणम् ।।
संघीभूयाभवन्नारी साक्षान्महिषमर्दिनी ।।१३।। ... ददौ सिंहं च हिमवान्रत्नानि विविधानि च ।। सुरया पूरितं पात्रं कुबेरोऽस्यै समर्पयत् ।। २८ ।। ... चेलुः समुद्राश्चत्वारो वसुधा च चचाल ह ।।
जयशब्दस्ततो देवैरकारि महिषार्दितैः ।।३२।।
ततोऽम्बिकां परां शक्तिं महालक्ष्मीस्वरूपिणीम् ।।
तुष्टुवुस्ते सुरास्सर्वे भक्तिगद्गदया गिरा ।। ३३ ।। ... तदैव क्षोभयामास त्रैलोक्यं सचराचरम् ।।
ततः क्रुद्धा महामाया चण्डिका मानविक्रमा।।५३।। (Shiva Purana, Uma Samhita)
On hearing the gods, Viṣṇu and Śiva were very angry. Their eyes rolled through anger. Then a great splendour issued forth from the mouths of the infuriated Viṣṇu and Śiva and from the bodies of other gods. The gods who were devoted to meditation on Durgā saw the mass of splendour blazing in all the ten directions. That highly terrible splendour issuing forth from the bodies of the gods joined together and became a woman Mahiṣamardinī herself. ... ... Himavat gave her a lion and gems of various sorts. Kubera a vessel filled with wine.... ... The four oceans shook and rolled. The earth quaked. Cries of victory were shouted by “the gods harassed by Mahiṣa. Then the gods eulogized the great Śakti, Ambikā in the form of Mahalakshmi with words choked with devotion. On seeing the world agitated, the enemies of the gods got up with uplifted arms and with their armies ready for war. ... ... He then agitated three worlds including the mobile and immobile beings. Then, Chandika of great honour and exploit became infuriated.
Thus Mahisamardini devi who is Shree Durga devi herself who is Shree Chandika herself is Shree Mahalakshmi. This is the reason while reading Madhyama charitra of Durga Saptashati it is told 'Mahalakshmir Devata' ie. 'The deity is Mahalakshmi'. Also the meditation of Mahlakshmi (dhyana shlokam) while reciting Durga Saptashati is done in her 18 handed form where she holds various weapons like Parashu, Gada, Padma, Dhanu, Danda, etc.. and at the end of dhyanam it is told:
सेवे सैरिभमर्दिनीमिह महालक्ष्मीं सरोजस्थिताम्॥
....I meditate on Mahishasura-Mardini Bhagwati Mahalakshmi sitting on the seat of lotus.
Kalika Purana describes Mahisasura had three births and Mahisamardini kills him in different kalpas taking three different forms. In his first birth, she kills her with her Ugrachanda form having 18 hands, in his second birth she kills her with her Bhadrakali form having 16 hands and in his third birth she kills her with her Katyayani form having 10 hands.
Thus from above it is proved that Mahisasura Mardini Durga herself is worshipped as Mahalakshmi and she is same as Chandika Parameswari also.
Other Aspects:
Sometimes Mahalakshmi is used to denote Matrika devi (like Brahmi, Maheswari, Aindri, etc..) For example this chapter of Agni Purana says:
Brahmā and other gods (should be worshipped) from the east to the north-east. (The goddesses) Brahmāṇī, Māheśvarī, Kaumārī, Vaiṣṇavī, Vārāhī, Indrāṇī, Cāmuṇḍā and Mahalakshmi should be worshipped from the east to the north-east.
This chapter of Garuda Purana also tells:
The image of Brahma has four mouths and is endued with a staff and Kamandalu (water-pot). That of Mahesvara has five mouths, ten arms, is seated on a bull with weapons as well as Matrika goddesses, such as Gauri, Chandrika, Sarasvati and Mahalakshmi. The image of the sun holds a lotus in the hand. Gana has the head of an elephant-Skanda has six mouths.
Also, a specific form of Rudra Chamunda Devi is also known as Mahalakshmi as this chapter of Agni Purana describes:
Hence she (is known as) Rudrachamunda, the goddess of dancing and one who is dancing. This (goddess herself), having four faces and in the sitting posture (is known as) Mahālakṣmī. (The goddess) having ten hands and three eyes (holding) (different) weapons, sword and ḍamaru (little drum) in the right hand and the bell, club, staff with a skull at one end and trident in the left (hand) and eating men, horses, buffaloes and elephants held in the hand is called Siddhacāmuṇḍā.
Similarly, there could be other specific forms in scriptures which are called Mahalakshmi and also various Sahasranamas or Shatanamas of various Devi might include the name Mahalakshmi in it.
How to Identify?
With the features described above, Mahalakshmi can be identified in a picture or idol or temple as:
If she is called Mahalakshmi but installed along with other Shaktis like Brahmi, Maheswari, Kaumari, she can be identified as Matrika Devi.
If she is called Mahalakshmi and is seated with Lord Vishnu, or holding lotus flowers in her hands, granting riches or worshipped with Lakshmi related mantras, she can be identified as Lakshmi Devi (Lord Vishnu's consort).
If she is called Mahalakshmi and is riding over lion, or riding over buffalo, or has 18/16/10 arms or holds Trishula, or is crushing Mahisasura or worshipped with mantras of Durga or Chandika or worshipped when Saptashati is recited, she can be identified as Mahisamardini Durga / Chandika.
If she is called Mahalakshmi and is presiding over Sri Yantra, or holding sugarcane, ankush, etc.. in her hands or is seated over Asana of Panchabrahmanas or is being worshipped with Sri Vidya mantras, she can be identified as Lalita Tripurasundari.
The above are just general features based on the descriptions present above. Some specific form could be identified based on mantra and its dhyana shloka only.
