As an adjective it implies a pertinance to the author of Alice's Adventures in Wonderland. The noun form (Carrol)is far more formalized, used only in instances where the subject is quite familier.
1: Used to describe someone who uses nonsensical words with relative ease.
2: A person who is capable of saying a silly or ridiculous sounding word or phrase without actually sounding ridiculous.
3: Someone who routinely replaces actual words with words like 'flibbertygibbet' or 'whatchamahoozit' yet somehow manages to convey the meaning of the intended word.
John recited the Jabborwocky for us in class today. He is surprisingly Carrollian.