Whether or not you recognize the name 'Don Johnson' is probably down to whether you were around to watch hit television shows during the 1980s. Johnson was one of the starts of 'Miami Vice.' which was definitely the best cop show of the decade. His career never really made it out of the 80s, and so he's a lesser-known name today. He only has himself to blame for that. He could have played John McClane in 'Die Hard,' and if he had, he'd probably still be starring in sequels today.
Johnson wasn't enamored with the script he read for the action movie, and decided that having been so closely associated with one police show, he'd rather not play a police officer in a movie. In doing so, he joined a list which includes Richard Gere and Al Pacino, who also turned 'Die Hard' down. That forced the producers to take a chance on the relatively-unknown Bruce Willis, and they never looked back.