Remington Steele - Season 1 Episode 10

Steele and Laura attend an island party thrown by a wealthy magazine publisher in order to learn why a client recently committed suicide. Soon, the party guests, as well as the host, begin being murdered one by one, until only the leads and the killer remain. At one point, when the situation gets dire, Steele tries to tell Laura more about himself, but Laura dissuades him, telling him that she would prefer not knowing about any crimes he might have committed before assuming the decidedly upstanding role of Remington Steele. The episode ends with Laura, Murphy, and "Ms. Wolf" humorously trying to get Steele to tell them his real name.