How should I tag characters that are essentially furrificated versions of an artist as a real person, not fursona in the usual meaning of the term? The artist goes by their real name, and that name is already reserved as their artist tag.

Example:
https://www.furaffinity.net/view/11751946/
https://www.furaffinity.net/view/28960418/
(cat lady)

Also, is there a specific tag for this kind of character?

Such characters are treated as furry personas because they are. Fursonas come in all sorts, from "what I wish I was" to "just me, but in a fur/scale/feather/something coat". Since, in the latter case, the fursona shares the same name as their artist, e621 tags them as name_(character).

Here's an example I normally deal with: British artist JollyJack represents himself in his art as a little hamster. We tag the hamster persona as Jolly Jack (character).

So, in the case of your example, we'd use roz_gibson_(character).