For simplicity's sake, I'm going off the "canon" of Krishna in the Mahabharata in its most common English translation that for whatever reason I have a copy of. Hinduism is ludicrously complex, there are thousands of texts and each deity has several versions, there is no one Bible that neatly contains most of the mythology.

Aside from the similarity in names

This is nothing but a coincidence. We know the origins of their names. Krishna means "black/dark blue" in Sanskrit. It's essentially an adjective for the color of the night sky. Krishna was very dark skinned, and when you see blue skin in Hindu art, it's an artistic representation of dark skin that might make it difficult to see facial expressions and such.

Christ comes from the Greek word Christos, which means anointed. It's a translation of the Hebrew word, "Meshiak", which also means anointed and entered English as "Messiah." There's tons of words between languages that sound similar and have 0 connection. For example, Liberia, Iberia, and Siberia sound like they have a similar root, when in fact they do not.

there are also very clear analogues in their nativity stories

Besides the virgin birth, a concept that exists in a lot of folklore, there are really few analogues. Krishna performed insane feats like lifting boulders as a baby. He went on to fight in wars. If anything, Krishna's story has more comparisons to Zeus, with Kansa being analogous to Kronos.

teachings

Jesus was a preacher. Krishna was a warrior prince who fought in the Kurukshetra War, he did not preach, however the Baghavad Gita is his dialogue with prince Arjuna, and it contains his lessons and some teachings etc.

the way they are a part of a trinity

Not really in the same way, and trinities are incredibly common throughout a lot of folklore. The number three is a nice number that works very well, especially for storytelling. We tell jokes in threes, we like three acts, etc etc. In the Christian trinity, you have the Son, Father, and Holy Spirit that are all distinct and yet the same being. The Hindu trinity is Brahma, Vishnu, and Shiva aka the creator, the operator, and the destroyer. Krishna is canonically the avatar of Vishnu, so he himself isn't quite part of it. Some believe Krishna to be his own separate deity. Mainstream Hindu belief is that every deity is another form of Vishnu (Vaishnavism). There's also another branch that believes Shiva to be the Supreme Being (Shaivism). Others believe they're all separate beings, a true polytheism. Others believe reality is feminine and is more goddess-centric (Shaktism), and that the traditional trinity are all women or are just husbands to the true female trinity.

while being incarnations of God and human at he same time

Whoever is making these connections is taking their upbringing in an Abrahamic mindframe and projecting it onto Hinduism. If there's any religion you can't do that with, it is Hinduism.

Also, there have been multiple branches and sects that have claimed Jesus to only be human. The entire Islamic religion reveres Christ as a holy prophet, but still as human.

Is it possible?

Anything is possible. But is it likely? Beyond a reasonable doubt, no.

edit: spelling