🔼The name Mahavite in the Bible
There's only one Mahavite in the Bible, and he is Eliel, one of the mighty-men of David (1 Chronicles 11:46). It's actually very strange that we know only one Mahavite, because the name only occurs in plural, preceded by the definite article: המחוים; the Mahavim. We also don't know where a Mahavite would come from; perhaps from an otherwise unknown place called מחו or מחה?
BDB Theological Dictionary entertains a few wild guesses from a few wild theologians: Perhaps this המחוים is a misprint and it should read המחני, which would denote someone from מחנים (Mahanaim). Or perhaps it should have read המעוני, which is Meunite; someone from Maon or Baal-meon.
We simply don't know what this strange plural ethnonym is doing here, but also note that the name Eliel occurs twice in close succession: 1 Chronicles 11:46 and 11:47. All this seems to suggest we're looking at a scribal error.
🔼Etymology of the name Mahavite
The compound המחוים consists of the definite article ה plus מחוים, which appears to be a plural adjective constructed from a noun מחו or מחוה. And that noun looks like it consists of the preposition מ, meaning "place of" or "instrument of" plus the root חוה:
Of all credible sources we usually consult, only Jones' Dictionary of Old Testament Proper Names dares to propose a translation of the name Mahavite (or rather, the plural Mahavim). Jones takes the preposition to mean "place of", and the חוה-part to refer to a tent village. Put in plural, Jones translates this name with Places Of Assembly. If we would apply the preposition to Eliel, this name could mean The One Who Gathers. Both explanations are long shots, though.