The general idea is to hide your identity initially. It's much more fun, and suspenseful, if you don't know who sent it to you, especially after you receive it! When you open it, if the sender wants to say who they are by including a card (which is usually opened last), then they will do that.
So, how does one maintain Anonymity? Well, the first and easiest way is to very clearly and obviously mark the box as a Rudolph exchange gift. If you see that it has that type of writing or pictures to that effect on it, then you can just avoid looking at the return address. Some folks will hide their return address, so you can't figure it out. And some folks will go out of their way to ship the package from another location entirely so the return address doesn't match their home anyway (like shipping the box while you are on vacation). You can have your spouse or significant other be on the lookout for the packages too.
And it's best practice, to wrap the gift(s) inside the box, so they can be removed from the shipping box (and placed under the tree. Again, this can be done be a spouse to make sure everything inside is good. If you have wrapped your presents, you should PM Rudolph, so he can inform your buddy that it's ok to open the box (or just write on the outside of the shipping box that the presents inside are wrapped, so they know when they receive it.)