I ask the instructor what I should log it as, and then I log it according to what they say. I don't care what they log....Most have said PIC or P1.
If *training* in a G reg, I log it as Dual received in my un-holy-FAA-logbook, if a club checkout I log it as Dual received and PIC, and funnily enough, if flying on my own, log it as PIC.
EA