US President Donald Trump suggested renaming the Strait of Hormuz the "Trump Strait", claiming the US now controlled the waterway, in a post on his Truth Social platform on September 2.

The remark was Trump's push to project American dominance over the world's most important oil chokepoint, even as the strait remains largely closed and contested in the war between Washington and Tehran.

"Now that we have it under U.S.A. control, should we change the name Hormuz Strait to TRUMP STRAIT???" he wrote, adding that it would be "hotter" than ever.

The suggestion followed Trump's claim a day earlier that the US held "almost total control" of the strait, an assertion at odds with shipping data showing most traffic through the route has halted.

Iran has maintained controls on Gulf shipping, laying sea mines and warning vessels against unauthorised transit, while a US naval blockade has cut off most Iranian crude exports.

The rhetorical flourish echoes Trump's earlier move to rename the Gulf of Mexico the "Gulf of America". It came days after US forces struck the Iranian island of Larak and Iran retaliated against US targets in Jordan and the UAE, and as US Central Command reported fresh strikes on IRGC targets in Iran on September 1.

The war began on February 28, when the US and Israel launched strikes on Iran and killed Supreme Leader Ali Khamenei. Iran responded by closing the Strait of Hormuz, through which about 20% of the world's oil and gas passed before the conflict.

Trump has a long history of demanding name changes of geographical areas, including, so far, the Gulf of Mexico, renaming that the "Gulf of America" and more latterly he demanded by executive action the renaming of the Lake Ontario to Lake of America. 

Trump has previously claimed that the Strait of Hormuz was US territory, in another social media post at the end of August to which Iran responded with strong language.