Puff Daddy/Puffy/P.Diddy has been around since before the 90's (1990 to be exact). He didn't "take" their name like you are suggesting so you should give that whole anti-P.Diddy argument a rest. It's pretty weak beyond the actual facts of the matter. I'm not saying you're not entitled to your opinion of the guy but if you're going to bash him at least do it legitimately.
Puffy AmiYumi is a decent group. I found out about them through a music video program that used to air after midnight on Much Music but I only started to take them seriously after seeing them in concert. Their english lyrics are pretty corny and I'm sure the translated Japanese lyrics are just as corny, if not worse (ie. average pop music). That said, they are musically coherent and that goes a long way as far as I'm concerned. Not great but pretty good. I'm not sure who I like more between them and a group like Shonen Knife but I'll give the edge to Puffy because they are more consistently good and overall less corny-sounding (if that makes any sense at all).
While we're on the subject, does anyone know if Puffy is still popular in Japan?