Are you a DVC member? If not, you will NOT be able to "link" the reservations. That means there is no guarantee that you will stay in the same room. As others have said you will need to check in for each reservation. You actually might have to change rooms for the second reservation.
You will also need to be careful that you have each of the people you are renting from handle their part of the trip. For example, if you are using Disney's Magical Express the first person will need to setup your arrival and the other renter will need to call and setup your departure. The same is true if you would like the Dining Plan, each will have to call and set it up for their reservation.
If you are a DVC member, this all changes. You can "link" the reservations, as long as they are for the exact same room type (in the same resort). Then you can take care of everything yourself and you will only need to check in once.
I have rented my points several times and even setup "linked" reservations with other DVC members. I have also had several conversations with DVC Member Services about putting two reservations together. My info comes directly from them.