Adam Clarke on Acts 18:8

Crispus the chief ruler of the synagogue - This person held an office of considerable consequence; and therefore his conversion to Christianity must have been very galling to the Jews. It belonged to the chief or ruler of the synagogue to preside in all the assemblies, interpret the law, decide concerning things lawful and unlawful, punish the refractory, excommunicate the rebellious, solemnize marriages, and issue divorces. It is likely that, on the conversion of Crispus, Sosthenes was chosen to succeed him.

Many of the Corinthians - Those to whom the sacred historian refers were probably Gentiles, and were the fruits of the apostle's labors after he had ceased to preach among the Jews.