We have a word for an adjective of a country: demonym, but do we also have a word for the adjective of a group? For example, people who belong to reddit are redditers, and this is an adjective for the group of reddit.
There are actually two words that come to mind here. Both of these primarily refer to people in a culture, or geographical area, but can also refer to a non-geographical group as well.
The first is exonymn
a name used by foreigners for a place, as Florence for Firenze.
a name used by foreigners to refer to a people or social group that the group itself does not use, as Germans for Deutsche.
The second term is endonymn
a name used by natives for a place, as Bharat for India.
a name used by a group of people to refer to themselves, their region, or their language, as opposed to a name given to them by other groups.
However, there isn't a term that encompasses both of these meanings, nor a word that negates the geographical implication. Also, being modern linguistic constructions, these words aren't found in any major dictionary.