Does your university name matter? If you are seeking an engineering job, do employers care about which university you attended? Do they look at your grades, or bias their decision based on the college's reputation? There are stories of Ivy League graduates struggling to find employment, while another person at a small, virtually unheard-of college grabbing that opportunity. So if you are attending a prestigious school, and your grades are lower than someone who is attending a small, high-school-like school, how will that affect your employment opportunities?
If you are seeking an engineering job, do employers care about which university you attended? Do they look at your grades, or bias their decision based on the college's reputation?


If you have a solid foundation in the skills that matter for your engineering discipline/sub-field, and can convey that to recruiters in a phone/on-site/on-campus interview, then I would say that to a first-order where you did your degree does not matter so long as you can get the recruiter's attention.

Getting the recruiter's attention is the trickier part for those coming from lesser-known schools. For example, at the engineering schools I'm familiar with, new grads can find a lot of good fresh-out career opportunities by attending on-campus engineering career fairs and the like. The downside of attending a lesser-known engineering school is that they may not have a decent attendance of engineering companies that come to the campus for recruiting purposes in the first place. This puts the burden on the student in getting a recruiter's attention. 

Engineering students (and students in other fields, I'm sure) from any institution can greatly benefit from networking with peers at other institutions and those already in industry. For those from lesser-known institutions, networking can be an invaluable tool for opening doors to career opportunities. Also, while obtaining an internship may be equally as difficult as obtaining a full-time position for those from lesser-known schools, participating in several internships along the way to obtaining your degree if at all possible (and performing the duties of the position well) would really go a long way to improving your chances of success.