Terry has said that the name ‘Ankh-Morpork’ was inspired neither by the ankh (the Egyptian cross with the closed loop on top), nor by the Australian or New Zealand species of bird (frogmouths and small brown owls, respectively) that go by the name of ‘Morepork’.
In The Streets of Ankh-Morpork and The Discworld Companion we are shown an illustration of the Ankh-Morpork coat of arms, which does feature a Morepork/owl holding an ankh. But from Terry’s remarks (see next annotation) it’s safe to say that neither bird nor cross were explicitly on his mind when he first came up with the name Ankh-Morpork.
Finally, many readers have mentioned the resonance that Ankh-Morpork has with our world’s Budapest: also a large city made up of two smaller cities (Buda and Pest) separated by a river.