I suspect it’s mostly a naming convention. Wars are often labeled after the territory where the fighting occurs rather than the actors involved. That’s why we say “Ukraine war” or “Iraq war,” even though multiple states may be involved.

In this case, “Iran war” is a bit misleading because the conflict is largely a missile and proxy confrontation affecting several territories (Iran, Israel, and parts of the Gulf), not just one battlefield.

Personally, I find it clearer to name conflicts after the primary actors involved. For example:

Russia–Ukraine war U.S. & Israel–Iran war

That makes the participants explicit instead of implicitly framing the war around a single country or location.