The first idea is that the existing name of your Zois is their “god-given”/”true” name. So that stays the same. However, you can give your Zoi a nickname, and give a toggle that decides whether friends call them by their nickname or by their true name. This would have far-reaching implications to be fair, because nicknames as primary names were a sign of “rabblerousers” or “punks” or whatever until after WWII. More than that, during the 1950s and 1960s this swap caught on as “normal”. However, since the trucker handle fad of the 1970s, through computer systems that we’ve used since the 1980s and a World Wide Web that made it stick around in the 1990s and 3rd Millennium, handles and usernames have returned that to normal to a degree… until social media muddied the waters so much that it seemingly no longer matters.
This can affect everything from mundane pre-industrial social trust to online identity to celebrity appeal to the kind of things seen in “magic”-based The Sims DLC.
The second idea goes with it. “Clubs” that Zois could join. These might require you to use either your Zoi’s true name or your Zoi’s nickname. Since it encompasses everything from Native American/First Nations nicknames to online handles, the nicknames will likely need Unicode support.