It is possible (for a player) to make a faction named 'Pirates'

[Trafalgar]

It is possible (for a player) to make a faction named 'Pirates', with the same spelling and capitalization as the existing NPC Pirates faction. This doesn't affect the existing Pirates faction in any way and they remain hostile, but it results in a PC faction with the same name. (I tried this on a server I did not have any special permissions on just to see what would happen)

I have not tried creating a 'Trading guild' faction, although I would not be surprised if that worked too.