Is it possible to change the name of an esp file? How do I change a character's height?

You can easily change the name of a .esp file-- on Windows it is just F2. However, be warned: if you have another Mod which needs to reference that .esp file, or a .bsa file associated with the Mod, they won't work properly if you change the .esp name. With the .bsa file, you can change the name to match the new name for the .esp, but modifying another Mod which depends on a certain .esp file is probably harder...

What character is it, and the context?

I believe the setscale command works in Skyrim like it did in Oblivion-- open the console, click the target, and then type "SetScale XX" where XX is a number.

If it is inside of a .esp, there should be a scale command inside the properties-- find the person you want to edit, and double-click on them. If you're planning to do this to the PC, I'd use the console.

Another note on this, a lot of files (Within a BSA or loose - doesn't matter) are in folders named after the esp file (Voice files, for one) so those will need to be renamed as well.

If you're renaming your own little esp file and the entire mod is currently just the esp, then simply rename it as described above. Done.