We used to put our company name and a phone number on the docs so the clerk would return them to us in case the document did not have an envelope attached to it.  Here the clerk requires a self addressed stamped envelope to return docs.  But most of the title companies have boxes or cubbies of sorts at the clerks office for them to return docs to us.  We stopped doing it sometime the beginning of the year because was giving away our clients, so to speak.
At the attorney's office  I do some work for, I put a sticker on the docs with our address so the clerk can send us back the docs but I do not put the examiner on the docs who is doing the recording.

I would just use a black marker and strike thru your name or address.  Unless the clerk would not allow that.  Adding the sticker already altered the doc anyway.