Does the college "name" matter when jobs start looking to hire you?

Yes and No. Its all about differentiating yourself.

Selectiveness doesn't matter so much as the quality of the school itself. There are schools that take a relatively large % of its applicants, Cornell and Georgia Tech, for instance. Likewise big state schools like Penn State are not as selective as say, Harvard or Princeton.

What's more important is that the school has a highly regarded program in your field of study. Which means lots of big state schools are often just as good as elite private institutions.

Job selection is competitive. Your resume is going to be on a large stack of other resumes. Going to a top school is a way to make yourself standout, but it isn't the only way. You could also stand out by having top grades. In fact, being top of your class at a lower tier school is usually better than being just average at a top tier school.

Another way, and probably better way, to standout, is work experience. Having internships or doing co-ops in your field of study is going to give you a tremendous advantage over people who didn't, even if they went to an extremely selective school.

While there are some people who will discount a person who didn't go to a top school, for the most part, I've found that a school's name can help you, but usually won't hurt you in the job process.

Some additional answers for you over here: https://careervillage.org/questions/1087/do-employers-hire-you-based-on-what-college-you-graduated-from