Rights of publicity protect a person's exclusive right to license their likeness to whom and on what terms they choose. This is at the heart of the NCAA student-athlete likeness antitrust litigation, because intercollegiate athletics may be the only place where this right is irrevocably transferred to the NCAA and its member institutions.
Fake Bo Pelini is a Twitter account designed to poke fun at the real Bo Pelini's sometimes surly and obstreperous nature. If the Fake Bo Pelini generates money from the use of Bo Pelini's likeness, he could be violating Pelini's rights of publicity. This does not appear to be the case.
The "Bo Pelini Foundation" is a registered trademark, but "Bo Pelini" is not. If "Bo Pelini" were a registered trademark or it was used on or in connection with goods or services, Pelini could not sue for trademark dilution, because Fake Bo Pelini is a parody account. If Fake Bo Pelini was not a parody and "Bo Pelini" were a registered trademark or used on or in connection with goods or services, then Pelini could sue for trademark dilution.