The name Brennan is a Gaelic baby name. In Gaelic the meaning of the name Brennan is: Brave. American Meaning: The name Brennan is an American baby name. In American the meaning of the name Brennan is: Brave. Celtic Meaning: The name Brennan is a Celtic baby name. In Celtic the meaning of the name Brennan is: Raven. Irish Meaning: The name Brennan is an Irish baby name. In Irish the meaning of the name Brennan is: Raven. Also 'Little drop; Prince.