The name Hachmoni in the Bible
There's a bit of a mystery surrounding the three names Hachmoni, Hachmonite and Tahchemonite. They occur only once in the Bible; all three together and in texts that seem to contradict each other (although usually when Biblical texts seem at odds with each other, there's treasure to be unearthed).
The name Tahchemonite occurs in 2 Samuel 23:8, where we learn the names of the mighty-men of king David. The first mighty-man mentioned there is Josheb-basshebeth, a Tahchemonite, who had slain eight hundred at one time. This man was also called Adino the Eznite (means something like He Who Delights In The Spear) for just that reason.
But in the parallel text of 1 Chronicles 11:11, the first mentioned mighty-man is Jashobeam (means something like Let The People Return), the son of a Hachmonite (identified as Zabdiel in 1 Chronicles 27:2), who once killed three hundred at one time. It's been suggested that perhaps the two are the same person.
But in 2 Chronicles 23:32 we learn of a man called Jehiel, who is a son of Hachmoni. He tutors the sons of David together with David's uncle Jonathan. Curiously, the personal name Hachmoni and the ethnonym Hachmonite are spelled identical. BDB Theological Dictionary, even, only treats Tahchemonite as ethnonym and reckons Jashobeam not a Hachmonite but a son of Hachmoni, just like Jehiel.
We'll probably never get to the bottom of this.
Etymology of the name Hachmoni
What we do know is that the three names Hachmoni, Hachmonite and Tahchemonite come from the root-verb חכם (hakam), meaning to be wise:
The name Hachmoni is the word hakam seasoned for sound with the vowel waw and postfixed with the letter nun, which is the common Hebrew construct that leads to a personification of the verb; wise + nun= wise-guy. The postfixed yod usually indicates either possession (wise + yod = my wisdom) or a ethnonym (Jerusalem + yod = Jerusalemite). The name Tahchemonite is pretty much the name Hachmoni prefixed with the letter taw, which works as an amplification or globalization (taw + wise = totally wise).
NOBSE Study Bible Name List only translates Tahchemonite, and does so with Wise. Jones' Dictionary of Old Testament Proper Names transliterates Tachmonite (without the first h and e) and translates Wisdom. Jones doesn't treat Hachmonite but reads Very Wise for Hachmoni.