What is a Byzantine church entrance hall called?

A Byzantine church entrance hall is called a narthex.

The narthex is a vestibule or transverse space at the western end of a church. It separated the main worship space, or naos, from the exterior and often provided an area for processions, preparation, and the participation of people who did not occupy the principal nave.

Byzantine churches could have an inner narthex, an outer narthex, or both. The outer narthex is often called an exonarthex. These spaces might contain doors, tombs, inscriptions, and painted decoration.

The narthex should not be confused with the bema, which is the raised sanctuary area at the eastern end. Nor is it identical to an atrium, an open courtyard that appears in some early Christian church complexes.