As far as I know, the names of the days e.g., Sunday, Monday, etc. are not found in scriptures like Srimad Bhagavatam. Say you want to find the day of week of Krishna's birth, it is not available.
Do the Vedas mention days such as ravivAra (Sunday), somavAra (Monday) etc?
Puranas do mention the names of days of week. For eg. Srimad Bhagvatam in 4.12.49 talks about Sunday:
पौर्णमास्यां सिनीवाल्यां द्वादश्यां श्रवणेथवा।
दिन-क्षये व्यतीपाते सङ्क्रमेर्कदिने पि वा।।
श्रावयेच् छ्रद्दधानानां तीर्थ-पाद-पदाश्रयः।
नेच्छंस् तत्रात्मनात्मानं सन्तुष्ट इति सिध्यति।। ( S.B. 4.12.49,50)
Persons who have completely taken shelter of the lotus feet of the Lord should recite this narration of Dhruva Maharaja without taking remuneration. Specifically, recitation is recommended on the full moon or dark moon day, on the day after Ekadasi, on the appearance of the Sravana star, at the end of a particular tithi, or the occasion of Vyatipata, at the end of the month, or on (Arka dine) Sunday. Such recitation should of course be performed before a favorable audience. When recitation is performed this way, without professional motive, the reciter and audience become perfect.
Here are some more refrences from Shristi khanda of Padma Purana:
यदाहस्तेनसप्तम्यादित्यस्यदिनं भवेत् ।
सूर्यस्यचापिसंक्रांतिस्तिथिस्सासार्वकामिकी ।।
4. That seventh day of the month which falls on (Adityasya dinam) Sunday with Hasta (rising on that day), and on which there is also the transition of the Sun, is the one which satisfies all desires. (Padma Purana chapter 25 "The vow of Adityasayana" )
यदासोमदिने शुक्लाभवेत्पंचदशीक्वचित् ।
अथवाब्रह्मनक्षत्रंपौर्णमास्यांप्रजायते ।।
तदास्रानंनरः कुर्यात्पंचगव्येनसर्षपैः ।
आप्यायस्वेतिचजपेद्विद्वानष्टशतंपुन ।।
4-5 When the fifteenth day of the bright fortnight (i.e. the full-moon day) falls on (Soma dine) Monday or the Brahmanaksatra appears on the full-moon day, a man should bathe with the mixture of the five products of the cow and with mustard; the wise one should again mutter the text ' (Please) grow' for one hundred and eight times. (Padma Purana chapter 26 "The vow of Rohini Candraiyana)
शुक्लांगारक संयुक्ताचतुर्थीजायतेयदा ।
श्रद्धयाश्राद्धकृत्तस्यांनप्रेतोजायतेनरः ।।
43. One who, with faith, offers a sraddha on the fourth day of a month which falls on a Tuesday in the bright half of a month, does not become an evil spirit. (Padma Purana chapter 32 "Descent of Holy place")
यदाचार्केगुरौसोमेवारे ष्वेतेषुवैत्रिषु ।
त्रीण्येतानिचऋक्षाणिस्वयंप्रोक्तानिब्रह्मपा ।।
72. Brahma himself has declared these three lunar mansions (to be auspicious) when they fall on Sundays or Thursdays or Mondays. (Padma Purana chapter 32 "Descent of Holy place")
The Mahabharata mentions about measurement of Time in terms of week also. Like:
O Bhishma, what is there remarkable in this one's having supported for a week the Govardhan mount which is like an anthill? 'While sporting on the top of a mountain this one ate a large quantity of food,'--hearing these words of thine many have wondered exceedingly. (Sabha Parva: Sisupala-badha Parva: Section XL)
One, who sees the lunar disc to have many holes like a spider's web, or one, who sees the solar disc to have similar holes has but one week more to live. One, who, when smelling fragrant scents in place of worship, perceives them to be as offensive as the scent of corpses, has but one week more to live. The depression of the nose or of the ears, the discolour of the teeth or of the eye, the loss of all consciousness, and the loss also of all animal heat, are symptoms indicating death that very day. (Santi Parva: Section CCCXVIII)
