according to the contents of python.el (the source file of python mode) run-python's `cmd` defaults to a function which returns the path and parameters of the system's default python version, and in turn runs this via `python-shell-make-comint`, so simply setting an unquoted name or trying to run a shell command directly won't work.

What works, however, is `M-: (run-python "python3")`.  It opens a new buffer with a python prompt.

Depending on which python version you usually run, it is even easier to set it in your `~/.emacs.d/init.el` and run it via `C-c C-p`, or to add those two variables as file-locals in a comment block at the end of a python file (excerpt from python.el's header):

<code>
;; … .  You can change
;; your default interpreter and commandline arguments by setting the
;; `python-shell-interpreter' and `python-shell-interpreter-args'
;; variables.  This example enables IPython globally:
;; (setq python-shell-interpreter "ipython"
;;       python-shell-interpreter-args "-i")
</code>