Palmer comes from an English surname meaning “pilgrim” which was originally used to refer to those who had gone to the Holy Land on a pilgrimage. Those who had gone would bring back palm leaves as proof that they had been there. The origin of the word comes from Anglo-Norman palmer via Medieval Latin palmarius via Latin palma (palm of the hand; palm tree, date tree) derived from PIE root word *pelə- (flat; to spread). The palm branch also has some interesting symbolized victory, success, or joy and has later come to symbolize peace as well. To the Assyrians and Ancient Egyptians, the palm tree also symbolized the Tree of Life, associated with the goddess Ishtar and is used in Christianity on Palm Sunday. In Greek, the word for palm tree is foínikas (or phoinix), which also means “purple, crimson” and is similar to the word for phoenix, as in the mythological word. From what I could find, Palmer has been used as male name but I can see it as a unisex name. Either way, it’s an interesting name with an even more interesting symbolism and origin in ancient cultures.