My wild hunch is public code names are mostly for show so the Secret Service can look cool and puff out its chest a little. And I assume when the president is abroad (etc) the services use hard/impossible to decipher code phrases because they could be intercepted by who knows what advisory or enemy. So in the US the service might actually say "Celtic is leaving the building." But if Biden is in Europe every important situation gets a different code and codes aren't reused.

That's my two cents anyway.