Actually the interesting thing is that it wasn't the Judeans that broke off from Israel it was the ten other tribes (other than Judah and Benjamin) that broke off and kept the name Israel while the remaining ones took the name Judah.
Which makes funny situation happen David and Solomon kings of Israel that ruled from Jerusalem but are protected by Gates of Samaria but not Gates of Jerusalem (If they get converted) (King Saul would also be protected by Gates of Samaria but he never ruled from Jerusalem since it was under Canaanite control at the time)
