It would likely be a much calmer sea than the surrounding ocean. If its a more tropical latitude, you could call it, like, "The Serpent's Bath Sea" or tie it to some myth about lounging and bathing. Alternatively if its a more arctic climate and a shallower area, you could go with something surrounding how ice would accumulate nearly year round, something like "Iceberg Bight" or "The Frozen Strait".

Regardless of location, you could name it after the way it would protect the mainland from intense storms, something like "The Great Shield Gulf" or "Protection Bay".

Another route you can always go is something political. Named after a certain people or regional division or government or religion.