Well, one member of the Cult is the Cult Leader, and can convert others to the cult; the other members are Cultists. The Victory condition is "Spreading the Good Word", i.e. that all surviving players should belong to the Cult. We can only convert, not kill.
Originally, I was a bog-standard jester.
On night one, I have no idea whom Takhisis tried to convert to the cult; he never told me before his death. Whoever it was, he failed.
On night two, Takhisis converted me to the Cult. I received a new role PM saying "You are a Cultist". The Cult is not called anything else except the Cult.
On night three, Takhisis, and this corresponds to the post where he said how busy he was, and with the fact that his frantic defense of himself comes to a sudden and unwarranted halt, forgot to convert anyone.
On day four, therefore, with Takhisis having been lynched, I received a new role PM, "You are the Cult Leader". This gives me the ability to convert a person every night. Therefore, on Night Four I successfully made a conversion, but there's no way I'm telling you who that was, because it is irrelevant to whether you believe me, I don't trust you not to lynch them, and if I did tell you I couldn't prove it was them, as, whoever they are, they would deny it if they had any sense.
On night five, I tried and failed to convert JR48Fan to my Cult. He is clearly not innocent, because why would a normal innocent be immune to conversion? Besides he would say he was innocent, wouldn't he?