there is no actual name attached to the engagement. It’s known simply as “Operation Praying Mantis,” not the obvious “Battle of the Persian Gulf.”
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Just like there is no “actual name” for the Battle of 73 Easting on 26 February 1991- the largest tank engagement in modern history.
I have a very good friend who was the Chief Gunners Mate on the USS Roberts in charge of the frigate’s missile battery that day. He has a great picture with the forward launcher which has Kill Marking painted on it representing Iranian ships. It was one of the very few naval engagements fought by the US Navy since WWII that resulted in the sinking of an enemy ship. It was a good day.