What is the origin ethnicity of the name Madden?

answer from ancestry.com

Madden - Irish (Galway): shortened Anglicized form of Gaelic Ó Madáin 'descendant of Madán', a reduced form of Madadhán, from madadh 'dog' (see Madigan).

Madigan - Irish: Anglicized form of Gaelic Ó Madagáin 'descendant of Madagán', from Madadhán, a personal name meaning 'little dog'. This name occurs chiefly in western Ireland.

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Maybe there is of German origin...