Does name of university matter for internships?
Some companies specifically recruit preferentially from top schools, some don't. All of them know that a 3.7 at one school isn't the same thing as a 3.7 from another and will make what they think are appropriate adjustments. 

But it isn't just about grades, and the only thing that will guarantee you don't get the internship is if you don't apply. Trying costs you nothing but a bit of time, and UCLA is a respectable school. Go for it; at worst it's good practice!