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1. Czech, Polish, Ukrainian, and eastern German (of Slavic origin): from the personal name Mach, a pet form of a vernacular derivative of Latin Matthaeus or Mathias (Czech Matěj, Polish Maciej, etc. (see Matthew)). In some cases, the Czech and Polish names represent pet forms of other names beginning with Ma-, for example Marek (see Mark) or Martin.
2. possibly also an Americanized spelling of Hungarian Mács, from a pet form of Máté or Mátyás, Hungarian forms of Matthew.
Jewish (Ashkenazic): unexplained.
3. Vietnamese, Cambodian, or other Southeast Asian: unexplained.

(Dictionary of American Family Names, Oxford University Press)
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