Does Trump have the legal authority to rename international bodies of water?

No. But since when has legality ever been a thing for him??😷

No.

Such re-naming normally needs agreement by all the bounding countries, the more so when their mutual frontiers pass through the water, or (for sea coasts) each nation's territory extends for some distance out to sea.

This is likely why President Trump's whimsical naming appears only on maps intended for use only within the USA. No-one else would recognise his new names.

I do not know if he really did intend re-naming the Strait of Hormuz; or whether that is an accusation by his detractors, of whom he does have a few. He can't! None of the Persian Gulf is anywhere near the USA, its feature names are purely for its own coastal nations to agree, and even the USA's allies there are hardly likely to accept Trump trying to claim them.

Incidentally I have seen on SW, photographs purporting to show tankers in the Strait of Hormuz. They were obviously false. The waterway is more than 30 miles across at its narrowest, not a mile or so as these images suggested.

Only for American maps. I find it bizarre though there will be new generations of people down the road learning this new map.

He’s only changing what American maps say.

The rest of the world still say Gulf of Mexico and Lake Ontario.