By 'rename' I assume you're talking about his practice of founding cities on the sites of pre existing minor settlements? The answer is pretty straight forward in that each city had two names. Alexandria, and a nickname to distinguish it from the others. These were either based on geographical location; for example Alexandria on the Oxus (river), Alexandria Eschate (the furthest) or named after the province they were in e.g Alexandria Arachosia, Alexandria Ariana.

As to how long the names lasted, some were abandoned relatively soon after the Hellenistic age, however some are still called Alexandria, such as Egyptian Alexandria and the previously mentioned Alexandria Arachosia, now known as Kandahar (developed from the local name Iskandaharia) or Iskandariya in Iraq.