moskeo

A moskeo is the place of worship of islamo. The building is defined by what happens in it rather than by its shape, though the shape is often distinctive: a prayer hall facing Mecca, a miĥrabo niche marking that direction, and frequently a dome and one or more minaretoj, the towers from which the call to prayer is given. Esperanto takes all four words from the international vocabulary, which is what it does with the technical terms of every religion.

The word is neutral and the register is encyclopedic. Moskeo is what you call the building; moskeano is not a word anybody uses, because the person is an islamano, a Muslim, and membership is of the faith rather than of the building. The parallel set is worth learning together: preĝejo for a church, sinagogo for a synagogue, templo for a temple, moskeo for a mosque. Only the first of those is built from Esperanto roots, preĝi plus -ej-, the place suffix, and the rest are borrowed whole.

Note that preĝejo is the generic as well as the particular. Literally it is just a place for praying, so it can cover any house of worship when you need a word that does not specify one. In practice speakers use it for a church and reach for the specific term otherwise, and that is the usage to copy.