It’s an old surname: a scribe Niketas Mavronis is recorded in 1285: Σημειώματα-Κώδικες – View Simeioma
The stem is pretty clearly μαύρος “black, swarthy”; the -vr- is something of a giveaway, and the name doesn’t particularly look Slavonic or Aromanian. (1285 is too early for Arvanite or Turkish.) The -ώνης could mean the surname is derived from μαυρώνω “to blacken”, but that looks forced.
Most plausibly, -ώνης is some sort of diminutive or name suffix. This site ΤΑ ΕΛΛΗΝΙΚΑ ΕΠΩΝΥΜΑ μια μελέτη και η Ιστορία τους. explains the suffix of Κοτσώνης Kotsonis as a diminutive of Kotsos < Kostas, adducing the colloquial diminutive (neuter) κλεφτρόνι “little thief”, and the surnames Γεωργιώνης, Γιαννακαρώνης, Διακώνης, Δροσώνης (from George, Big Little John, Deacon, Fresh [proper name]).