I expect they're using some kind of authentication framework that supports full names in its User entity, and just went with that without considering whether it's sensible.

Looks like you can leave comments on prayers? Could also be that they want a particular aesthetic where everyone has their innate "Christian Name", instead of a username, which is assocated with left wing ideas like digital utopianism. Because...

Real names also enforce a complex of related authoritarian information structures i.e. they provide information about a person's culture, race, gender, which you can use to assign them a place within your religion's moral hierarchy.