My understanding is that the Kingdom of Naples never existed under that name on paper. There was the Kingdom of Sicily, and after Sicily revolted during the Vespers both parts claimed to be the legitimate Kingdom of Sicily, one with capital in Palermo and the other with capital in Naples (hence the "Kingdom of the Two Sicilies" label when they were finally reunited). *Naples was considered a Papal fief still during the 1490s so I suppose that the original Kingdom of Sicily was one.
And when were the royal titles for kings of Sicily, Naples etc created?
Best Regards
Grey Wolf