Does name of university matter for internships? I have been recently applying for summer internship positions in the engineering discipline. I am a senior undergraduate at UCLA university. My GPA is above 3.7 and I have both desired and minimum qualification for the internships, but I keep receiving rejection email from different companies. I was told by my friends that since students from Stanford, Berkeley, MIT and other more prestigious schools than UCLA are applying, therefore they get the internship first and if there is any opening hiring managers will consider people like me.

I would like to know: is this really true and does the name of such universities compared to UCLA make a huge difference?
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!