You got downvoted, but I agree. "Gen" is very typically used as a shorthand for "generate", whereas I've _only_ seen it used as a shorthand for "generic" in the Erlang/Elixir world.
I have sympathy for gp. But also, naming things is hard. Wait till you dig deeper into the erlang rabbit hole and discover the undocumented gen module.
IDK, I don't live in Elixir and that name trips me up every damn time I need to read/write some. Everywhere else, "gen" is typically a shortening of "generate" (which I don't love either—just write the word—but it's fairly common), and "generic" rarely occurs in code at all (elsewhere related to programming, yes—in code, no)
[EDIT] incidentally, as long as I'm complaining about Elixir, I've done a lot of Ruby and have no clue whatsoever why people act like Elixir is similar to it, yet constantly see "oh yeah, it's so easy for Rubyists because it's so similar". Then again, I haven't done any Phoenix with Elixir, so maybe they just mean Phoenix is Rails-like.