For undergrad, your bigdest concern should be grades, not where you go. It's pretty much the same for med school (grades, board scores, etc) for getting the residency you want. The only time school name might make a difference is if you want to go into academic medicine, then it might help to go to a higher ranked med school.
So no, name doesn't really matter. Of course you might argue that you can get a better education at certain schools...