If you modify a ref type (in preferences) and put a period at the beginning of the name, it will hide the ref type (at least in X9.3 and earlier). You can also remove/delete an individual field name by editing a ref type, and it won’t appear (unless the field already contains information in a pre-existing record and then it will show that info, with the generic field name in that record).
But rearranging the order of the fields has been a long time request and early on when developers actually spoke to us users, they indicated that this was difficult due to the database structuring.