Final answer:
The catechumens became known as neophytes after their initiation, highlighting their new beginning in the Christian faith, influenced by ancient mystery cult rites.
Step-by-step explanation:
When the initiation was complete, the catechumens became known as neophytes, or beginners in the faith. This initiation process, similar to those of ancient mystery cults, involved various rituals leading up to Christian sacraments such as baptism, which was viewed as a purification and incorporation into the church. The shift to a more secretive practice of Christian rituals reflects an alignment with the ways ancient mysteries, including the Eleusinian Mysteries, valued secrecy. Baptism and other Christian sacraments began to mirror the initiatory processes of ancient mystery religions in their confidentiality and symbology, despite early Christian rejections of pagan practices. The catechetical lectures by Church Fathers such as Cyril of Jerusalem and the practice of referring to the Eucharist as 'Mystery' are indications of these influences.