(covers information from several alternate timelines)
The Bering Sea was a sea on planet Earth, which bordered the North American region of Alaska and Union of Soviet Socialist Republics (Russia). The Arctic Circle passed through this sea. There were a small number of large islands in this sea. (Star Trek IV: The Voyage Home; Star Trek; Star Trek: Enterprise opening credits)
In the 17th century, the Bering Sea region had not yet been explored by European explorers. The region was within an area known as the "America Septentrionalis". (Star Trek: Enterprise, opening credits)
In 1986, the humpback whales George and Gracie were released back into the wild in the Bering Sea. The whales were rescued from whale hunters by the timely intervention of the HMS Bounty. (Star Trek IV: The Voyage Home)
Background information Edit
Information on European exploration was from the 17th century map "Harmonia macrocosmica seu atlas universalis et novus, totius universi creati cosmographiam generalem, et novam exhibens", which was created by Andreas Cellarius. A scan of the original can be found here.
This sea was labeled on a 21st century-era political map of Earth seen in the remastered "The Cage". This was a Central Intelligence Agency map published either in April 2007 or September 2008. The difference, which was not noticeable at the resolution of the image from the episode, was the addition of Kosovo, which gained its independence between the releases. The label "Bering Sea" was not legible to the viewer.
Retroactive continuity: A 20th century-era map of the North Pacific Ocean was stored in the USS Enterprise library computer in 2254. The Bering Sea was labeled on this map. This map was among the materials viewed by the Talosians when they scanned the Enterprise computer. (TOS: "The Cage")