What was Aphrodite's surname?

Urania.

The Greeks didn't use surnames per se. The secondary name used for describing a diety represents a specific function or attribute. "Aphrodite Urania, or the celestial Aphrodite was the goddess of pure and ideal love. Aphrodite Genetrix or Nymphia favored and protected marriage....Aphrodite Pandemos (common) or Aphrodite Porne (prostitutes) was goddess of lust and venal love...Under the influence of her legend Aphrodite later became a marine diety (Pelagia, Ponte)." ("Larousse Encyclopedia of Mythology")
When diffrencing between persons of the same name, the Greeks would add the person's place of origin. Homer uses the additions Cytheriaen (of Cythera) and Cyprian (of Cyprus) to describe the goddess.

According to the Handbook of Classical Mythology Aphrodite's surname was Pandemos, but personally I thought it was Urania.