en_tn_lite_do_not_use/luk/02/05.md

to register

This means to report to the officials there so they could include him in the count. Use a term for an official government count if possible.

along with Mary

Mary traveled with Joseph from Nazareth. It is likely that women were also taxed, so Mary would have needed to travel and be registered as well. (See: rc://en/ta/man/translate/writing-participants)

who was engaged to him

"his fiancee" or "who was promised to him." An engaged couple was considered legally married, but there would not have been physical intimacy between them.