I found an old thread from tree years ago about giving characters who do not have an official name a character: tag.
https://e621.net/forum/show/167492
<adjective>_<species>_(<artist>) and <species>_(<artist>) have been suggested, but there is no definitive answer. (And instead of "artist" it should probably say "character owner" instead.)

In my particular case I found post #1672947, wanted to see more of this character but had to go through the character owner's FA gallery and manually search for individual posts on e621.

So far I have found these posts:
post #1672947 post #1570473 post #1504910 post #356294 post #956097

It would be useful to tag these posts with a character tag so it is easier to find posts of this character, but as far as I can tell, the character owner did not give this character a name.

Can we decide on an official system to handle these situations?

The schema suggested in the old thread, furred_dragon_(underscore) in this case, does not seem too bad.

I would also suggest a more generic schema: unknown_character_(<owner>)_<number>, where <number> is a number which is incremented for each new unnamed character by this owner. So unknown_character_(underscore)_1 in this case. This also lends itself nicely to searching with wildcards. The currently highest number could be written down on the owner's wiki page.

Calimero000 said:
as far as I can tell, the character owner did not give this character a name.

On a small handful of posts they're referred to as "Rocket" in either description or third party comments.
For this particular character I'd suggest rocket_(underscore)

Calimero000 said:
I would also suggest a more generic schema: unknown_character_(<owner>)_<number>, where <number> is a number which is incremented for each new unnamed character by this owner. So unknown_character_(underscore)_1 in this case. This also lends itself nicely to searching with wildcards. The currently highest number could be written down on the owner's wiki page.

This gets way too computery and extremely hard to remember, or search, in any possible way, so no.

Best example coming to my mind is manmosu marimo. I don't know who started the tagging system on their characters, but if I'm searching for the white dog character, I'll simply search all character tags with (marimo) in the name like this and woah, I can immidiately see that I'm looking for character that's white canine, not the student pup, where with your suggestion, I would need to manually open up all the tags for the characters to know which one is for wich and even then not knowing, because many of the characters are featured in same images and usually paired!

Just like with artist tags, where there's no definitive rules on what to use in all cases, simply go with what's most useful and least likely to get confused. If there's absolutely zero information of what the character name could be, then describive adjective + species + owner sounds and has been the best approach.

I wouldn't worry too much of wildcard, as it's much better approach to figure out the character first, then search and wildcard is easy still because artist would be in (), making search not confuse it with the artist tag.

Calimero000 said:
I would also suggest a more generic schema: unknown_character_(<owner>)_<number>, where <number> is a number which is incremented for each new unnamed character by this owner. So unknown_character_(underscore)_1 in this case. This also lends itself nicely to searching with wildcards. The currently highest number could be written down on the owner's wiki page.

This also feels me with horror and dread :)

For the character in question, I too found a picture where he suggests that 'rocket' is the correct name: (https://www.furaffinity.net/view/27985598/ ) ... however, if that didn't exist, I'd say underscore_(underscore) since he refers to it as "me" a few tiems as well.

Mairo said:
Just like with artist tags, where there's no definitive rules on what to use in all cases, simply go with what's most useful and least likely to get confused. If there's absolutely zero information of what the character name could be, then describive adjective + species + owner sounds and has been the best approach.

I generally agree with this. short_white_rabbit_(underscore) can be descriptive enough for finding further images. Even Orange_male_cat_(underscore) would work, if there was an orange_female cat to contrast with.