adherence - noun
- attachment or commitment to a person, cause, or belief.
devotion - noun
Love, loyalty, or enthusiasm for a person or activity.
Religious worship or observance.
fellowship - noun
- Friendly association, especially with people who share one's interests.
See also: association, commitment, affiliation
EDIT: I had a feeling that the words I had provided weren't exactly what you were looking for, so I did some further research. According to textproject.org the term Demonym is not limited to geographical implications:
A person can have many demonyms. If she belongs to a club or a sports team, she may have a demonym that describes that interest. She may have a demonym that comes from where she lives or goes to school. A person can have as many demonyms as he has interests and community connections.
The demonym of a fan group can come from the history of the group or a symbol unique to that group. Do you love to listen to music by Beyonce? Then you may be a part of the “BeyHive.” The demonym BeyHive is a play on Beyonce’s name. The Bey part of Beyonce sounds like bee, the insect. It is as if Beyonce’s fans are bees following the queen bee, or, as Beyonce is sometimes referred to, the “Queen Bey.” The demonym BeyHive takes advantage of the unique spelling and pronunciation of Beyonce’s name.
In the article I linked they cite another non-geographic example: Fans of the Green Bay Packers are called "Cheeseheads."