The artifact should be listed in your artifacts list (which you can't access when pushed up against a wall by a demanding quester, and which doesn't show the English names anyway). Thus, your choice is completely blind unless you have an old legends mode export handy. It's quite possible the artifact was brought to a visitor who died at the embark (which happens a lot due to old age if sieges doesn't kill them).
The artifact is probably not one of yours, as it ought to have some kind of relation to whomever is looking for it. Due to the buggy behavior of questers, not giving up the artifact can be a bloody affair, as questers tend to come in groups, and one of them can leave and try to sneak in to steal it, and if you engage the thief (regardless of whether the thief attacks or try to flee) the fortress erupts in chaos as the other members of the quester group (which I call "infiltrators") scare dorfs at a minimum so they run around fleeing. Infiltrators have 3 behaviors:
1. Continue with their business of socializing, praying, etc. Dorfs still get afraid of them.
2. Run around in panic scared of all the scary dorfs, who, in turn, run around in panic scared of the scary infiltrator.
3. Attack civilians while still claiming to go about their business (i.e. socializing, etc.).
In none of the cases are the infiltrators marked as hostile, so it's a pain locating them. However, stationed militia will detect and engage them. Given that most of them have behavior 1 and 2 most of that is rather one sided, but the ones from group 3 can cause quite a mess.
I've also seen corpses of non military type visitors after such a mess, and I suspect those were visitors who, for whatever unknown reason, decided to get involved on one of the sides.
In my current fortress questers seem to have given up (with me not having released any artifacts), and return to apply to become mercs and monster slayers (I've tagged the members of the larger quester groups using DFHack's gui/rename to keep track of which questers belong to which groups when I have to deal with them as they turn out to infiltrators). I've also seen that the quester group memberships shift around, so returning questers can end up in different groups.
It can also be mentioned that questers (with their associated infiltrators) can just try to steal an artifact without ever having requested it, so you can suddenly be alerted to the detection of a thief and then get cancellation spam as your dorfs run around scared of the infiltrators you might not even be aware of cause a mess in your tavern (and open temples).