Urgent! We need to extend "alt_name=..."!!!!111^^

https://xkcd.com/1864/

From the title text of that comic (hover over the image to get a tooltip) the actual tag would be “demonym=…”

Maybe more a neologism, than a demonym ?

There’s also a nickname tag:

https://taginfo.openstreetmap.org/keys/nickname

because it’s not always derived from name, for example:

https://en.wikipedia.org/wiki/Big_Apple