if they were going to change the name it would be gootube. but i doubt they will change the name, but I bet they will make the video quality much better
They should just leave it as YouTube but they'll probably add a logo or two of their own, just like yahoo on flickr.
Google has already said that YouTube will remain a seperate business entity, so there is no plan for them to integrate it into the Google network of products. I think that's a very smart idea, YouTube is well branded and should try to stay as "un-tainted" by Google as possible.
Just for fun: how about YooooouTube ? Or just replicating on searches the Gooooooooogle model on Next/Previous browsing?
GooTube and GTube sound gd to me but personally i still prefer it to stay as youTube. haha.. its already so well-known and easily remembered by all.