I think Denti way back on page 1 had it right. I think it would be P2 for the pilot who was not the designated commander.
Rudestuff. Different companies and national agencies rules may (will!) vary but I can see various scenarios where two captain could fly together. For example, I heard of a Royal Flight in the Middle East where all the pilots were both captains and all were right seat checked to ensure maximum flexibility. Alternatively a captain who needs landings for recency so the trainer occupies the right seat and acts as PM for both sectors. I’m sure there are other examples.