There was a Judah, which later claimed to be a major Israelite tribe...
OK, here is the question, if a group broke away from Israel, wouldn't that group be called something else, and Judea be called Israel? Why did Judea change its name, if it was the original Israel, with the political and religious capital given to it by God?
Many historians argue that the United Monarchy of Israel is a myth. That when Israel was conquered, educated refugees brought Israelite stories to Judea. Even if it was not a myth, the United Monarchy only lasted for about 70 years with Jerusalem as its capital. For most of Israel's history, Samara was the political capital, and Mount Gerizim
That being said, Judea/Judah definitely existed for about a thousand years. The Jews definitely were in Southern Israel, and expanded out over all of Israel, including the West Bank. They were weaker in Gaza, where the Philistines/Greeks were stronger. Much of that expansion included conversion, so todays Jews are definitely partly descendent from the Israelites who stayed behind in what today is Northern Israel.
And yet England was united by Wessex(West Saxons), you would think the Saxons would name their kingdom after themselves.