Best way to see it...maybe...I guess?
For as many times as I have stopped to help someone find a disc, or have given back discs found to those who said it was theirs(regardless if I knew it was), I will not ask another person or group of players if it is their disc. If they look like they have lost a disc, then yes, I would bring it up to them, as in "I just found a disc, or looking for a disc." If the disc has a name or #, I just don't have the energy to call someone who may of lost it. I may ask my boyz if they know this person.
Now if I see the disc in an area I know discs might be landing, then I may sit around to point it out to players coming up. I remember one day I walk up on a lost disc as soon as another guy did, and he asked if it was mine, and I said it was his now(like let him decide what to do with it).
Now at a league or tourney event, I will leave it with the director.
Personally, I hate throwing other's plastic, especially with names/#s. Many times, I just give the discs to some less fortunate looking youths. I tell them to enjoy, and if you get sick of it, give it to another kid, or just call the owner. Keeping the whole transaction safe, informal, and in good spirits.
If I lose a disc, I am not going to get too far without trying to find it. If I can't find it, good luck to those who do, and hopefully it's a less fortunate kid. Discs are not like wallets. To me, if you can't find it, go buy another one, get your throws under control, don't be throwing where you shouldn't which is almost always where I and probably others found it in the first place (i.e. WATER, NASTY ROUGH, HEAVY WOODS, maybe use spotter next time). All in all, the best thing is to hope it gets in the rightful hands some day, which may not always be the rightful owner.
If the disc meant that much too you, then you shouldn't throwing it, or at the very least be putting markers on it in the first place. As we can all agree, generally, the top products(discs) in this sport are $20max(basically a night out at the bar you let get away).
Sorry if I made anyone feel like what I am saying sounds shady. And for the record, I do not have any people's discs with their names on them in my possession, as they have all been donated or given back to the owner.