Whether to buy a used bow or not isn't impacted by the presence or absence of another bowhunter's name for me.
Now, if the seller indicated there was no name on the bow but he'd be willing to put his name on it before shipping, I'd ask him not to. So I prefer there is no name.
I think I've only had my own name on one new bow and I don't remember asking for it. I wouldn't have my name put on another.
IF/When I truly identify a life-keeper and I intended to pass it down to one of my grandchildren, I might consider having my name put on that bow. If my Dad had been a bowhunter I would love to own a bow that he had used and bore his name.
BIAS ALERT: Surely there are some names (and nicknames) that I won't accept on my bow, my binoculars, bow blind, my arrows, or anything else I own. In fact, I won't even consider buying something with "Bone Collector" or "Crush" on it. Thank goodness the "traditional" bow market is of no interest to these marketers.