There's a fort (Fellglow Keep) where mages experiment on vampires. I saved a vampire who otherwise would have been killed; I noticed after the fight that she was standing up in her cage. To release her I made her a follower (I use AFT) and commanded her to teleport to me.

So now I have a follower with the rather impersonal name "Vampire Fledgling".

I wonder if anyone knows a console command to re-name her. I know there is such a command in Oblivion.

I'm not aware of any console commands to do so and a cursory look at the commands listed on the wiki doesn't reveal anything telling.

You'll likely need some form of mod in order to achieve this.

there is one mod that lets you rename almost everything in game you should look for it search rename skyrim on google surely google will find you the mod you want

Be careful about renaming generic NPCs, altering their names can affect every other NPC using the same base in the game.

Try Jaxonz Renamer.

It can only rename followers if I don't use a follower mod, so I'm stuck with "Vampire Fledgling", apparently.

But it can still be useful, so I'm going to download it anyway

And if you rename her before you make her a follower, doesn't that work?

Yes, very useful mod, I rename mainly horses and containers.

The thing is, I've already made her a follower.

Anyway, she has mysteriously disappeared so it doesn't matter. I think follower mods don't work very well with generic NPCs. She has probably "de-spawned" or something.