Yes and no. It's not too uncommon to hear some sloppy grammar in quick, informal speech, such as in your example But your example only "works" when the contraction "there's" is used. The same sentence with "there is", though it's essentially the same, sounds much more wrong.

It's perfectly fine --and grammatically correct-- to say "there're just so many names..." in quick, informal speech.

There are is absolutely correct here. But in conversation, using there's like this is extremely common.