If they have a name, I'd tag it even if it's the first post. The character tag isn't gonna hurt anyone.
If we have to come up with a name for them, for me it would come down to the volume of the artist's posts and the proportions thereof. If a character is a one-off (or a couple images at once that can be parented), there's no point naming them, and if the artist only even draws one character the tag is less useful, but for an artist that has multiple OCs or a lot of art in general to filter through, anyone with multiple posts deserves a tag IMO. It's just a matter of how difficult it is to come up with an appropriate tag name and whether it's worth it, but I don't think I'd ever fault someone for making a tag or be upset at one's existence.
So TL;DR if you're asking the question and have a tag name in mind, make the tag. Or at least that's my position.
(Also do people like...Actually search for the OC tags anyway? Not that it really matters when it comes to filtering, but I'm lowkey curious now about the statistics.)
I do search for OC tags. Not all the time, but for example itou has a bunch of established OCs and enough post volume overall that the chartags help if you're looking for a specific image or a particular girl.