I recently created WebDAV remote to my annex which I assumed to be just for testing purposes at the time, so I gave it a strange and long-wided name. It turned out, though, that the remote is stable, works fine, and that I'm going to keep it. Now, I would like to give it a snappier and more descriptive name than the one I originally chose. Is that possible somehow?

You can rename a git remote with just "git remote rename ". However, for a special remote, git-remote will fail to rename it unless you first add a dummy remote..fetch value in .git/config. You can remove it later.
So, for example:
(The webapp handles doing this when you edit a remote's name, BTW.)
There's actually another place the name of a special remote is recorded, in
remote.log. That name is only used when you usegit annex initremotethough. It actually is possible to change it, by usinginitremoteto change the vale of the name field. Example:Note that for some types of special remotes, this will require you to re-specify some other configuration. For example, with a directory special remote, it wanted me to include a directory= parameter.