You could use any of these three. 'Enrol' tends to be used for longer-lasting lists - you enrol (or 'enlist'*) in the army, but register for a day-school. But that's only a tendency - you could use either in either situation.
To my ear, 'registering' for something is more suitable when the activity is more direct (e.g. online), whereas 'being registered' suggests going up to a table or filling in a form - with a clerk of some kind doing the actual thing. But again, this is just a personal view, and the two are effectively equivalent in many cases.
*Despite the generic appearance this verb has a specific meaning. An 'enlisted' person is enrolled in a military organization.
Student or Learner