Did you follow John Cakars’s advice to look up in the book A DICTIONARY OF JEWISH SURNAMES FROM THE RUSSIAN EMPIRE?

The author found the name in Dvinsk (Daugavpils), Latvia, in early 20th century.
Gostini is halfway between Riga and Daugavpils.

The letters CH are pronounced like in German (or KH in Russian or Scottish loch).

The origin is from Biblical Enoch, in Hebrew Hanoch or Hanokh.
Yiddish addition of diminutive L made it Hankhel, Henkh’l or Henkhl.
Russian has no H and regularly replaces it with a G: Genkhel.

Polish or German transliteration make it GENCHEL.

English speakers would pronounce it like Gentchel.