Do I have to give maaser from money that I recieved as a gift from someone who already takes maaser from their money?
Yes. The obligation (or custom) of giving maaser depends on the person who receives the income, and not on the money.
Sources: Taz, Yoreh Deah, 331:32; Ahavas Chesed, chap. 18, in the name of Eliyahu Rabbah, Orach Chaim 156.