"Gayvoronskiy", "Gayvoronskaya", and "Gayvoronsko" ("may be spelled with an H depending on location)" are Slavic surnames relating to Haivoron, Ukraine; meaning "Son of", "Daughter of", and "Child of Haivoron". 
Men.
This is a list of relevant men with the surname "Gayvoronskiy" or "Hayvoronskiy;"
Women.
This is a list of relevant women with the surname "Gayvoronskaya" or "Hayvoronskaya";