Being "pre-med" in undergrad doesn't mean anything 98% of the time. In the vast majority of institutions there is no such thing as a pre-med major; it really isn't especially common because it doesn't mean anything if you don't get accepted to medical school.

Some colleges and universities do have official pre-med programs, but most don't. Probably the majority of colleges and universities do have pre-med advisors and loosey-goosey type pre-med clubs/organizations, but you don't have to be a member of it to go to medical school, although it usually can't hurt. You don't have to have a piece of paper that says "bubbleprncess—pre-med from the University of Kentucaliflorida" to apply to medical school. All you have to do from an undergraduate perspective academically speaking is take the right classes, most of which are offered by almost all colleges and universities, and take the MCAT.

You can get a degree in absolutely anything you want and usually it won't make a difference. To get in to medical school, from everything I've read (which is a lot), the best advice academically speaking is: major in something you're interested in AND that you can get good grades in—if you're interested in the subject then you're more likely to do well in the classes, take the right classes whether they are part of your major curriculum or not, score well on the MCAT, and get good grades no matter what.

If you go to Random University that doesn't have an official pre-med program (like I said most don't anyway) and also doesn't have a pre-med club/organization/advisory service, it's really not a problem as long as you've got the grades, the classes, the MCAT score, the extracurriculars, and good interviewing skills. Major in what you want to major in.