The expression "nom de plume" is not the original
French. The French for "pen name" is
nom de guerre.
The English expression was apparently created by someone who knew just enough French to know that "guerre" meant war and "plume" meant pen, but no more.
Another English term is by-name. Yet another English word for it is pseudonym, which is actually the most straightforward English name for the thing: it's a pity it looks dauntingly learned.
However, it is reported that "nom de plume" is now used in French, for specifically the pen name of a professional writer (i.e. not just any alias): evidently a recent re-import from English.