The "P" that PIAPRO gives to some of the members of its community (full-width ASCII, not a normal capital "P") stands for "Producer". It is used as a respectful honorific to take the place of a normal honorific like さん (san) or 様 (sama). Not only is this true, it is also a term only to be used for people whom PIAPRO's management has deemed worthy of the title.
Because of the fact that most Western VOCALOID Producers don't speak or read Japanese, we are mostly unable to join PIAPRO and have a chance to receive this title. However, the Western community has collectively agreed that very large VOCALOID communities such as VocaloidOtaku.net, and VOCALOIDism.com (i.e. not this site yet) have the ability to also grant this title to Western Producers who have made at least one original VOCALOID song that is considered by the community to be worthy of admiration.
What does this mean? It means that the "P" should only be used by people other than yourself as a term of respect if, and only if, the administration of one of the aforementioned sites has agreed that you can be called by this title.
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I'll try not to get on people's case for adding the "-P" to their own names when talking about themselves, even though it can come across as extremely pompous or arrogant.
However, I don't think it should be allowed to use the honorific if the title has not been given to the Producer rightfully. In fact, I think it would be best to disallow the use of a "-P" in usernames altogether, but I'm not in a position to make that call.
Thank you for your attention,
~Just Koda