We've discussed the Makabim / Maccabees - now what is the origin of the name חשמונאים Chashmonaim / Hasmoneans?
There are a number of theories:
a) According to the Jewish Encyclopedia, Wellhausen this was the name of the grandfather of Matityahu (Mattathias). The 1911 Encyclopedia Britannica writes of "Asmoneus, or Asamonaeus (so Josephus), great-grandfather of Mattathias"
b) Some associate the name with the locations Chashmona חשמונה (Bamidbar 33:29) or Cheshmon חשמון (Yehoshua 15:27). According to these theories, the family lived in or near one of these places before moving to Modiin.
c) Another theory connects Chashmonaim to chashman חשמן. It is unclear what the word chashman means - it appears only once, in Tehillim 68:32. Some explanations of the word do not fit a connection to Chashmonaim - for example Ehrlich says it may mean horses or chariots. However, the Septuagint translates it as "ambassador" and other commentaries have "princes". Therefore the name Chashmonaim referred to the status of the family, and the author of Maoz Tzur picked up on this - אזי בימי חשמנים . This approach was adopted by the Radak and the Meiri, but Amos Chacham in Daat Mikra finds it very far-fetched.
From this interpretation, the word chashman developed into the meaning of "an important person", and eventually became the translation for the Catholic "cardinal".