As I understand it, both sides had prefixes: Baja and Alta. After the US took Alta California, they dropped that prefix. Mexico was never forced to add one.
They dropped the prefix because Mexico wasn't in a position to object. I wouldn't be surprised if many expected at the time that the newly founded US state would annex Baja eventually.
We had that opportunity -- the guy negotiating the treaty decided San Diego was far enough.
counterpoint: the Indian state of West Bengal and the country of Bangladesh (lit. Land of the Bengali).