From SuspireWiki

Domain is an area of a city (or the city itself) that is claimed by a vampire, or vampires.

This could also refer to the Domain Merit.

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(n., traditional)

The physical territory claimed by or granted to a vampire, especially when that territory is officially sanctioned by the Prince; also, a conceptual purview of authority or responsibility wherein the lord has control or unique rights, such as the “domain of medicine” or “domain of theater.” “I don’t care what your Prince says, asshole, this is my domain, and every monster around here knows it.”