Renaming the Current File in Vim

The command is called :saveas, but unfortunately it will not delete your old file, you'll have to do that manually. see :help saveas for more info.

EDIT:

Most vim installations have an integrated file explorer, which you can use for such operations. Try :Explore in command mode (I would actually map that to a function key, it's very handy). You can rename files with R or delete them with D, for example. But pressing <F1> in the explorer will give you a better overview.

If you use git and already have the tpope's plugin fugitive.vim then simply:

:Gmove newname

This will:

1. Rename your file on disk.
2. Rename the file in git repo.
3. Reload the file into the current buffer.
4. Preserve undo history.

If your file was not yet added to a git repo then first add it:

:Gwrite

I'm doing it with NERDTree plugin:

:NERDTreeFind

then press m

To rename you can choose (m)ove the current node and change file name. Also there are options like delete, copy, move, etc...

• Write the file while editing - :w newname - to create a copy.
• Start editing the new copy - :e#.
• (Optionally) remove the old copy - :!rm oldname.

On Windows, the optional 3rd step changes a little:

• (Optionally) remove old Windows copy - :!del oldname.

Short, secure, without plugin:

:sav new_name
:!rm <C-R>#  // or !del <C-R># for windows

control + R, # will instantly expand to an alternate-file (previously edited path in current window) before pressing Enter. That allows us to review what exactly we're going to delete. Using pipe | in such a case is not secure, because if sav fails for any reason, # will still point to another place (or to nothing). That means !rm # or delete(expand(#)) may delete completely different file! So do it by hand carefully or use good script (they are mentioned in many answers here).