Is it required to be an ATP and work for an airline to be a Captain?
The key phrase, legally speaking, is "pilot in command".  On a multi-crew aircraft the PIC is normally given the honorific title of Captain, but what really matters is the legal status of PIC where an aircraft legally requires more than one crew.  In general to be PIC of a multi-crew a/c you need an ATPL.  Operators may operate single-pilot aircraft like Caravans as if they were multi-crew with two pilots and call the PIC Capt, but again that's just an honorific title and in that case the PIC can be just a CPL.

Like DLH says, a PPL or CPL can call themselves anything they want; Captain, Great Exalted Poobah, Zontar The Munificent, whatever.