Help with filling contracts

[Selena Stew]

For the P&S contract for both the owner (seller) and buyer. Do I need to put my name and/or assigns under buyer for the owner's contract. Then name and/ or under seller for the buyer's contract. I understand that P&S contracts are assignable by default so I just want to make sure I did everything accurately. Or do I would I put something like contract vendor.

Next I will be giving the P&S contract I had with the owner to the buyer's title company. This is the correct thing to do, right?