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.

Seems to be convention. If you search for "Russian war", the top hit is "Ukraine war", second hit "Ukraine-Russia war". Most results seem to mention both parties but when brevity is needed, the place where it's taking place seems to take priority over the belligerents

Just observing, not saying it's a good or bad linguistic practice

That would made it hard to distinguish all the wars US started, threatened or will start.

Because we're sitting here on the American side. In Iran it's probably called the America war or the Israeli war.

Another way to name wars, when they aren't happening to you, is based on where they happen. The war is happening in and around Iran. It's very unlikely that Iran will manage to bring the war to America. You could also call it the Gulf of Persia war.

You can also name them propagandistically, as in the "2023 Israel-Hamas war". Thankfully this hasn't happened in this case.

The US is involved in too many wars to call them all the "US war".

Point of view. If you are American its the war with Iran. If you are in most other English speaking countries you would go along with that. That said, I have also seen it referred to as "the Middle East war" and one headline calls it "Trump's war".

I wonder what they call it in Iran?