If they called it 'generic_server' then people would make fun of it for being too verbose. If they call it 'gen_server' then everyone pretends they know what it means and stays quiet.
I associate “gen” more with “generation”, in the sense of “gen Z”. In any case, it’s confusing.
With code completion you shouldn’t have to resort to abbreviations (unless they are already part of the (business) domain language). This was different in the 1980s though.