Set of DAG vertices disconnecting a vertex from forbidden vertices
Wikipedia says that, for an undirected graph, you can say:


$A$ is the vertex separator for $v$ and $F$.
$A$ is the separating set for $v$ and $F$.
$A$ is the vertex cut for $v$ and $F$.


perhaps these terms are used for digraphs as well, even though "connected components" are not quite the same thing in digraphs.

edit:  @PålGD suggests the variant "separator", similar to the second option.