Given a relation $ R \subseteq A \times B $.
from wikipedia: The domain of R is the set of all x such that xRy for at least one y. The range of R is the set of all y such that xRy for at least one x.
Hence: $domain \subseteq A, range \subseteq B$
A cannot be called domain, since that name is taken by one of its subsets which is only equal to it in special cases. If you insist on calling A the domain then my new question is: what is the set of all x such that xRy for at least one y is called?
Wikipedia mentions "set of departure" for A and "set of destination" for B. But I am wondering if people would understand and accept if I would use those terms.