I think you're referring to a specific retelling, maybe from a modern collection? The classic old Arabic anecdotes about Abu Nawas don't have a structured 'story' with a fixed cast. It's more of a historical and literary figure surrounded by tales. The key character is obviously Abu Nawas himself—the witty, hedonistic poet who outsmarts authority, usually the Caliph Harun al-Rashid or his vizier, Jafar al-Barmaki.
Those two, the Caliph and the vizier, are his most frequent foils. Their straight-man authority sets up Abu Nawas's subversive humor. Sometimes you get minor characters like a stern judge, a rival poet, or a tavern keeper, but they're just props for the joke. The real dynamic is the triangle of power, intellect, and mischief.
I've seen some modern novelizations or TV dramas try to invent a fuller supporting cast—loyal friends, love interests, a jealous enemy—but that feels added. In the core anecdotes, the cast is minimal because the focus is purely on the verbal duel and the punchline. The charm is in that simplicity, honestly.