Yes, there is, but you need to understand both contextual concepts to the word Logos in Christianity and its equivalency in Hinduism. In the Christian Bible it states - "In the beginning was the Word, and the Word was with God, and the Word was God" The 'Word' being 'Logos'. The first concept is that the Logos and God were One before creation and the Word was the first manifestation of God, and the personification of God is the Word. The first manifestation of God in creation was the Word, and Jesus is the Word and Jesus is the incarnation (avatar) of God. Jesus and God are One.
The first concept, that the Word was the first manifestation of God, is in Hinduism. Swami Vivekananda writes (Complete Works, Vol 3, section Bhakti Yoga, subsection The Mantra: OM: Word and Wisdom; available here - https://advaitaashrama.org/cw/content.php):
In the universe, Brahmâ or Hiranyagarbha or the cosmic Mahat first manifested himself as name, and then as form, i.e. as this universe. All this expressed sensible universe is the form, behind which stands the eternal inexpressible Sphota, the manifester as Logos or Word. This eternal Sphota, the essential eternal material of all ideas or names is the power through which the Lord creates the universe: nay, the Lord first becomes conditioned as the Sphota, and then evolves Himself out as the yet more concrete sensible universe. This Sphota has one word as its only possible symbol, and this is the (Om). And as by no possible means of analysis can we separate the word from the idea, this Om and the eternal Sphota are inseparable; and therefore, it is out of this holiest of all holy words, the mother of all names and forms, the eternal Om, that the whole universe may be supposed to have been created. But it may be said that, although thought and word are inseparable, yet as there may be various word-symbols for the same thought, it is not necessary that this particular word Om should be the word representative of the thought, out of which the universe has become manifested. To this objection we reply that this Om is the only possible symbol which covers the whole ground, and there is none other like it. The Sphota is the material of all words, yet it is not any definite word in its fully formed state. That is to say, if all the peculiarities which distinguish one word from another be removed, then what remains will be the Sphota; therefore this Sphota is called the Nâda-Brahma. the Sound-Brahman.
Now, as every word-symbol, intended to express the inexpressible Sphota, will so particularise it that it will no longer be the Sphota, that symbol which particularises it the least and at the same time most approximately expresses its nature, will be the truest symbol thereof; and this is the Om, and the Om only; because these three letters (A.U.M.), pronounced in combination as Om, may well be the generalised symbol of all possible sounds. The letter A is the least differentiated of all sounds, therefore Krishna says in the Gita — "I am A among the letters". Again, all articulate sounds are produced in the space within the mouth beginning with the root of the tongue and ending in the lips — the throat sound is A, and M is the last lip sound, and the U exactly represents the rolling forward of the impulse which begins at the root of the tongue till it ends in the lips. If properly pronounced, this Om will represent the whole phenomenon of sound-production, and no other word can do this; and this, therefore, is the fittest symbol of the Sphota, which is the real meaning of the Om. And as the symbol can never be separated from the thing signified, the Om and the Sphota are one. And as the Sphota, being the finer side of the manifested universe, is nearer to God and is indeed that first manifestation of divine wisdom this Om is truly symbolic of God. Again, just as the "One only" Brahman, the Akhanda-Sachchidânanda, the undivided Existence-Knowledge-Bliss, can be conceived by imperfect human souls only from particular standpoints and associated with particular qualities, so this universe, His body, has also to be thought of along the line of the thinker's mind.
In Hinduism, therefore, the Sphota, OM, is the equivalent of the Logos. The Aitreya Upnaishad I.i.1 (Swami Nikhilananda translator) says:
In the beginning [all] this verily was Atman only, one and without a second. There was nothing else that winked. He bethought Himself: "Let Me now create the worlds."
The other concept that Logos identifies with is the personification of the Godhead through an incarnation. Christian theology says there has only been one incarnation- Jesus. Hinduism, on the other hand, says that there have been several incarnations, and will be in the future. Krishna says in the Gita, Chapter 4 verses 7-8 (Swami Nikhilananda translator):
Whenever there is a decline of dharma, O Bharata, and a rise of adharma, I incarnate Myself.
For the protection of the good, for the destruction of the wicked, and for the establishment of dharma, I am born in every age.