I, personally, never used the term “pen name” because I much prefer the term “nom de plume”
I am likewise fond of the term “nom de guerre”, and although not as commonly adopted into English (only 7 hits on Google) I will often choose to use the term “nom d’etage”.
Now, I figure the French must have a similarly cool term for the names we assume for ourselves whilst anonymously harassing each other on the internet (I hope I’m not shattering any illusions here but, E.g. it don’t say bienville on my driver’s license).
(Autonateur = poncy french attempt to come up with a non-english word for computer that you have to use in official correspondence with the cockpockets whenever you have the misfortune to deal with them or their government).
“Stage” in English has many meanings, and is rendered by different French words. The theatrical “stage” is not “etage”, though - it’d be rendered by théâtre or, if you mean the literal stage where plays are acted out, scène, or even more physically, les planches. “etage” sounds like a literal, incorrect, Babel-fish like translation to me.
I’d call it a screen name. That term applies more to AIM that to a message board, but I think it’s still valid. What would be a French translation of “screen name”?
That would be “ordinateur”. And I would add that, as weird as it may seems to you, we don’t call a vacuum cleaner “vacuum cleaner” but “aspirateur”’, a plane “plane” but “avion”, nor a satellite dish “satellite dish”, but “parabole”. I could cite hundreds of other examples. For some reason we feel the need to use non-english names for nearly everything. Including, big surprise, computers. How weird!
As for the OP, I don’t know of any french word with the meaning he’s searching for. Anyway, most internet-related words are borrowed from english.