When I flew as a flight instructor there was no such thing as a 'right seat endorsement'. Rather, an instructor will initially receive dual instruction when doing their rating so that can learn how to fly accurately from the right seat.
As others have mentioned, you can fly from either seat unless the POH states the PIC must sit in a particular seat (only tandem seat aircraft such as the Decathlon come to mind). Whether this is wise is up to you to decide i.e. can you reach the fuel selector from the right seat?
Again as others mentioned, only the PIC logs the time during private operations. Don't be like a pilot I came across who logged any time they flew in a right seat as 'co-pilot'. They had hours ranging from ultralights to twins but didn't even have a PPL.