How about religionym?
While there could be something that better differentiates between "name of a religion" and "name of a religious adherent", I think it's a better choice then demonym for several reasons:
- it's more specific
- it's likely to be more meaningful to the casual reader because the root word is more clearly visible
- it does not appear to contain the word "demon", which may cause the casual reader to make unintended and likely incorrect associations
While the word is not as common as demonym and ethnonym, I've found religionym used in some academic publications, such as Reisigl, M. and Wodak, R. (2001) and even defined in Kader, N. (2016) - see Appendix 1, Table 2, p. 45 (pdf p. 20 of 28)
Reisigl, M. and Wodak, R. (2001). Discourse and Discrimination. Rhetorics of Racism and Antisemitism. Routledge: London. Retrieved from https://books.google.com/books?id=WP2CAgAAQBAJ
Kader, N. (2016). A Critical Analysis of Anti-Islamisation and Anti-immigration Discourse: The Case of the English Defence League and Britain First. International Journal for Innovation Education and Research, 4(5). Retrieved from http://ijier.net/index.php/ijier/article/view/538