Complex sentence: Thereafter, if not before, Liber was inextricably identified with Bacchus and Dionysus, and his name used more-or-less interchangeably with theirs: all such cults came increasingly under the official control of Rome's censors and "pontifices" (senior priesthoods).
Split into simpler sentences: Thereafter, if not before, Liber was inextricably identified with Bacchus and Dionysus. His name was used more-or-less interchangeably with theirs and all such cults came increasingly under the official control of Rome's censors and "pontifices" (senior priesthoods).