"Nacho Mama's" is actually a reasonably amusing pun. There's nothing amusing or clever in a bad respelling of póg mo thóin.

Chi-Chi can be a nickname as well as a euphemism (in addition to world famous golfer Chi-Chi Rodríguez, there's MLB pitcher Chi-Chi Olivo), so "Chi-Chi's" is actually a plausible name for a restaurant. The same can't be said for "Pogue Mahone's". "Pogue" is a (rare) Irish surname, but it's never used as a given name.