en_tn_condensed/act/18/08.md

Titius Justus ... Crispus

These are names of men. (See: rc://en/ta/man/translate/translate-names)

leader of the synagogue

a layperson who sponsored and administered the synagogue, not necessarily the teacher

all those who lived in his house

Here "house" refers to the people who lived together. Alternate translation: "the people who lived with him in his house" (See: rc://en/ta/man/translate/figs-metonymy)

were baptized

This can be stated in active form. Alternate translation: "received baptism" (See: rc://en/ta/man/translate/figs-activepassive)