This is how it ought to be according to the official rules:
The official convention for naming atoms is that an
"X-onium" atom is composed of a particle and its
whereas an electronic atom formed with an X+
as its nucleus is called "X-ium".
Examples are "protonium" (p+p-)
vs. "protium" (p+e-)
and "positronium" (e+e-),
the last of which cleverly qualifies under both conventions.
But this isn't the way it is! The µ+e- atom (chemical symbol Mu) is not called "muium" but instead is called "muonium", which properly ought to refer to µ+µ-. Why? The excuses are as follows:
Still another term, "exotic atom", is generally reserved for atoms with normal nuclei in which an electron has been replaced by a heavier negative particle. The least exotic type is the muonic atom µ-Z, in which the negative muon often (for high atomic number Z) orbits so closely about the nucleus that other electrons and neighbouring atoms "see" the muonic atom as essentially a slightly enlarged and "fuzzy" nucleus of charge +Z-1 and atomic weight A+0.113 (the muon mass is 0.01126 of the proton's). But that's another story.