It is not an acronym. It is indeed an abbreviation for 'facsimile.' FAX is a common mis-rendering.

Aside: This is the reason I keep half-joking/half-serious mentioning we should take back the name "fax" and recycle it as a better, easier/more-fun to say, vocabulary for 3D Printers. They build 3D facsimiles, thus they are fax machines and a 3D printed object (for which no good terms exist) is a fax. There's enough context shift not to be confusing with old school 2D fax machines. (Allowing of course, for silliness like GL(tf) over modem creating new "fax numbers" and some intentional confusion for amusements sake.)