The name of the renter should be on the prined confirmation and will DEFINITELY need to be on the reservation itself or you wouldn't be allowed to even check-in (be sure tho have photo ID with you). However ... until you have checked in, the reservation will under the full control of the member who owns the points - renters will not be able to make any requests or changes to the reservation. You should expect and ask for a copy of the printed confirmation letter in your name. You should be able to call the reosrt directly a few days ahead of arrival to confirm your reservation.
Enjoy!