The Rabinowitch trick (in Eisenbud's Commutative Algebra with a view toward Algebraic Geometry, page 132) says that $R$ (commutative unital ring) is Jacobson if and only if for every prime ideal $P \subset R$, if $(R/P)[b^{-1}]$ is a field, then $R/P$ is a field. Equivalently, each quotient domain $S = R/P$ has the property:

(*): $S$ is a field or the intersection of its nonzero primes is $(0)$.

Does this property (*) have a name?