I think that the initials M&M have been sufficiently well used by various entities throughout history that they could not hope to prove that the name originated with them. Given that part of maintaining a trademark is defending it against encroaching use the existence of other corporate M&M companies, M&MDirect for example, would lead to their lawsuit failing.

Swim Shady, on the other hand makes no sense at all as a name if Slim Shady wasn’t already a well known thing.