I have rented out confirmed reservations and had exactly this situation.
First, I went in and used the 'Modify' feature on the online program to remove the rest of my family from the reservation, leaving only me, because I am in the Primary position. By removing everyone else, I think I make it less confusing and less work for Member Services. Then I added the name and address of the person I was going to rent it to. Only the renter who would actually become the primary person. Then (and this is a step that is extra) I also went in and changed MY address on the Reservation to their address. So now their address was listed with them, and with me. Why? Because next, I called up member services and asked them to take my name off and move the person in second position into primary. I am not sure how the Member Services program works, but I figured it would be easy for them to just delete my name and put in his name, if I had the same address information (and phone number and email) for both of us. But, maybe they just have a button to delete everything for one person, in which case they would delete mine and move his up. I was just trying to make it easy for Member Services, so they would have less retyping to do. Once member services put the new person in the primary position, they asked me if I wanted to add anyone else. I told them no, not at this time. (again, just trying to save them work). Then I went into the Modify program once again and added everyone else on the reservation.
The reservation number did not change.
The reservation had been linked to my own
MDE account and also the accounts of multiple other members in our family, who were listed in the reservation. Once my name and their names were removed, then it was no longer linked to our MDE accounts.
I hope this helps.