I’ve been working for parishes for a dozen years.
We do know Canon Law WRT things like parish boundaries, the term “register” is pretty much a term in the US which means “get in the parish database”.
We have people who live in other parish boundaries who register, when, for instance, they have a teen prepping for Confirmation, we contact their official pastor and get his permission for the Sacrament to be conferred here. Some Diocese offer blanket permission for these “Roaming Catholics” to receive Confirmation, Baptism, Marriage, at other parishes inside the Diocese. Other Bishops have very strict rules about registering at a parish that is not yours.
One of those things parish staff does behind the scenes that Joe and Sally Pewsitter do not have to worry about.