What is the Greek myth in which a hunter recognizes his loved one who has been transformed into deer and kill it?

The myth you are referring to is the story of Actaeon and Artemis. Actaeon was a skilled hunter who accidentally stumbled upon the goddess Artemis bathing in a sacred pool in the forest. As punishment for seeing her naked, Artemis transformed Actaeon into a deer. In his new form, Actaeon was chased and killed by his own hunting dogs, who did not recognize him.