The only free and comprehensive online etymological dictionary of the Spanish language
dama (1) f. (Noun) "lady"

13th cent. Borrowed from French dame "dame." From Latin domina "lady (of the house)." See dueño.

Romance: Western Vulgar Latin: Portuguese dona, donzela, Galician dona, doncela, Catalan dona, donzella, French dame, demoiselle, Italian donna, dama; Eastern Vulgar Latin: Aromanian doamnã, Romanian doamnă, damă; Sardinian dòna