Before calling himself J. Cole, his original rap names were Blaza and then Therapist.
When J. Cole first got down with Bomm Sheltuh (as in, Bomb Shelter), he used to go by the rap name Blaza. But they all agreed the name had to go, so he dug through the dictionary and ended up with the name Therapist. However, a name like Therapist was quite problematic during the Myspace era, because when you see a URL like myspace.com/therapist it kinda looks like his name is The Rapist. Arrested Development fans know what we mean. He eventually adopted the moniker J. Cole before dropping The Come Up.