Come to think of it, I don't hear about it as often as I probably should.
Government officials, the news and people in other professional contexts call it Gqeberha, frequently struggling with the click sound, even when a "k" sound will suffice.
Otherwise, I still hear people call it "P.E."
"Port Elizabeth" was still kind of a mouthful
People I meet from the Eastern Cape just say they're from "the Eastern Cape", because unfortunately most people don't know where Nxuba or Makhanda is.
Hell, a lot of people think Gqeberha/P.E. is the capital city of the Eastern Cape. (Bhisho is the capital)