Thing about Famicom is that ファミコン was, at the time, a trademark of Sharp for something else - think it was a microwave or a convection oven - and I think Nintendo was worried about that, so they just went with the full name and figured that most Japanese people would abbreviate it, as Japanese people do, to the first two syllables of each word, and they wouldn't need to officially call it "Famicom", people would just call it that anyway. (Note that in the 8-bit era, they never actually used the name Famicom...but Sharp's licensed version DID.)
A few deals with Sharp and they managed to get the trademark, so the 16-bit successor became Super Famicom.