The term "sphinx" is a transliteration of the Egyptian (Old Coptic) term meaning "living image", so could easily refer to any statue. The Anubis idea is often put forward, also a more conventional lion. Clearly, the head has been recarved, since even those who won't accept the water erosion evidence are faced with the much worse erosion on the body compared with the head, which has been exposed to the elements while the rest of the statue has been covered with sand for most of the thousands of years since it was built. This is Colin Reader's take on it: