Of Swords and Parasols

Basically: She started a detective agency, but learned no one wanted to hire a female PI(remember: 80s) so she invented a fictional boss named Remington Steele who was always "out of town." He was a con artist who, in the midst of conning one of her clients, stumbled across HER con, and recognized a good gig when he saw one, and assumed the role of RS. She realized a somewhat controllable figurehead was good for business, ad that she couldn't risk his exposing her, so she let him. He never told her his real name(eventually, we learn he's an orphan and doesn't know his own name) and she gave him the nickname of "Harry," which he liked. Later, the man who raised him showed up(the actor, BTW, was Stephanie Zimbalist's RL father) and when he heard about that, he told her that he'd also given Steele the same name when he was a child.