presumably a riff on git, the well known famously unsuccessful version control system
Huh, I had no idea. (I'm not a native speaker.)
DoIt isn't really a swear word. It's a euphemism for coitus. It's also a very common phrase in general so it really isn't strongly associated with "doing it" to cause any issues with English speakers. Aka it's fine as a project name. See Nike's "Just do it." advertisement campaign, they would have never gone with the phrase if it had strong negative connotations.