Yup. They could just call it "Obay" (as in "obey") for that 1984 feel, or "Obae" (i.e. "bae") for the anachronistic language use or something. Don't get me wrong: these puns are not especially funny, but they also literally took me 5 seconds to come up with as a non-native speaker, are not any dumber than "Ogay", and are completely devoid of any discriminatory undertone.
"Obay" is honestly pretty good, both as an anti-corporate/advertising (which works great with a female lead and potentially plays into her characterization) or like you said as anti-authoritarian.
If you want a fucking lame pun then just change it to `O-laid`. Still retains it's 'sex joke' and doesn't offend a particular group!
I dig this too.