Rename Current File

Vim doesn't come with an easy way to rename the existing, current file. The closest you will get with a one-off command is :saveas {new file name} which renames the current buffer, but also leaves you with your old file.

Another approach that you can take is to chain two commands together. You can start be deleting the current file (don't worry, you've still got the file contents in your buffer) and then saving the buffer with the new name. Like so:

:call delete(expand('%')) | saveas new-file-name.txt

While this seems to do the job well enough, your mileage may vary. Consider using a more robust plugin, such as vim-eunuch or rename.vim.