In reply to:

terms such as Nutmeggers and Hoosiers are called "nicknames" and the others such as Mancunians and Texans are called "sobriquets".


I think we need something more specific. Since nobody has come up with anything, why don't we coin the expression "adjectival toponyms" for them? I did think of toponymic adjectives but decided that would probably be adjectives used in place names such as High Wycombe and New Zealand .

Bingley



Bingley