radar bubble suggests itself
for referring to such an intersection (at least if this intersection is not the empty set, if the two events under consideration have accordingly a suitable causal relation to each other).
A plain web search for "radar bubble" along with "intersection" and "light cone" suggests that this terminology is used only rarely (at present; while, surely, such intersections are discussed more frequently).
Therefore my question:
Do we perhaps have another, more conventional name for referring to the intersection of the future light cone of one event, and the past light cone of another event (in suitable causal relation to the first event) ?