what is the name of the entity that iran and oman created to control the strait

The entity was the Persian Gulf Strait Authority. It was reported as an Iran-created body established in May, with rules requiring ships to register under a newly instituted Iranian insurance scheme for the Strait of Hormuz.

What it does

The reporting says Iran used this authority to tighten control over shipping through the strait, including registration and insurance requirements for vessels.

One important note

There are also reports about Oman being involved in routing or coordination discussions for transit through the strait, but the named entity created by Iran in the reporting is the Persian Gulf Strait Authority.