I noticed that for all recordings, every player has to be mentioned by name. On one of my runs I played with 3 other players who aren't users on this website. Is my run Null if they don't have an account here?

You can submit the run and put their names that they have while you played with them. They will appear as "guest" in the run, and it's allowed.

Please note that you will still need to have all evidences in your own recording if they didn't record their POV.