For some reason, renaming the current buffer file is a multi-step process in Emacs.

(defun rename-current-buffer-file ()
  "Renames current buffer and file it is visiting."
  (interactive)
  (let ((name (buffer-name))
        (filename (buffer-file-name)))
    (if (not (and filename (file-exists-p filename)))
        (error "Buffer '%s' is not visiting a file!" name)
      (let ((new-name (read-file-name "New name: " filename)))
        (if (get-buffer new-name)
            (error "A buffer named '%s' already exists!" new-name)
          (rename-file filename new-name 1)
          (rename-buffer new-name)
          (set-visited-file-name new-name)
          (set-buffer-modified-p nil)
          (message "File '%s' successfully renamed to '%s'"
                   name (file-name-nondirectory new-name)))))))

(global-set-key (kbd "C-x C-r") 'rename-current-buffer-file)

This defun fixes that. And unlike some other alternatives to perform this common task, you don't have to type the name out from scratch - but get the current name to modify. Like it should be.