Nearly every time I'm asked my name, my answer is immediately followed by another question, usually "Where's that from?" or "What does that mean?"
Recently, I've answered the first question by saying, "It's the Latin transliteration of the Hebrew name which Matthew is the Greek transliteration of" which is more honest than saying "It's Hebrew" but also may be more than most people want to know, and doesn't really give them much that's useful to go on.
When I have more time, I tell the story of Mattathias of Modin and his sons, the Maccabees. The way I tell this story has also changed considerably over time, and changes with my audience.
I don't think I've ever satisfactorily answered the second question, and I don't think anyone else has either. What does it mean that I am named Mattathias (and not perhaps Matthew or Methuselah)? Has the name become a part of me? Have I become a part of it?