I know three or so Ps, like, pretty well.
AshiotoP, HokeP, and I think Osamu-san.
AshiotoP really, really... uhm... I use UTAU better than them. Their P name was given to them by someone after they noticed they were the only Japanese user who used Ashioto Kori.
Aside from his usernames, he generally refers to himself as AshiotoP at ANY given chance.
I think to him, receiving a P name was like a bragging right.
(And as I said, even though he has made one or two original songs with help from others, and has made a few USTs... I use UTAU better than he does.)
I can't really judge Hoke-san's work (aside that his mixing is AWFUL and he can't use LOKE well. At all.), but his P name is just his name with a P at the end. I've only seen him use it in video descriptions, and I stalk his blogs and twitter.
I don't know if he makes his own USTs, since I'm not good at stalking him. I also have no idea if he's made original songs or not. (But, I really have a feeling that he hasn't.)
Osamu-san may not actually have a P name, but I'm pretty sure he does 8D;
He has, like, ten original songs posted on his youtube page.
I've only seen one hint that he might have one, and that was a P name in the tags on the video for one of his original songs on nico.
He's a member on Piapro (And I think he was emoing about something piapro related recently?)
Anyway, if he has a P name, he really, really doesn't show it off or brag about it. And I'm sure he has one, since he has a ton of original songs and junk.
(Actually, one of my favorite UTAUs was voiced by TanukiyaManbow~ He makes a HECK of a lot of original UTAU songs, and quite a few are like "LOVELOVELOVELOVE", and I don't think I've ever even seen him use a P name.)
BUT, I stalk Japanese users every chance I get, SO.