The surname (at least if we talk about people of Jewish origin) seems to mean a person from the place called Golovenchichi (Головенчичи in Cyrillic) or - Yiddish version - Golovenchitzy (in Russian transcription - Головенчицы or in Belorussian transcription - Галаве́нчыцы) in Belarus. There are 3 places in Belarus called like that (Golovenchitzy) : 1. Near Grodno, 2. Near Stolbtsovo (in Minsk Region), and 3. Near Chausy (in Mogilev Region). Ariel Sharon's mother was born in the latter one.