First of all, back in late-1985, early 1986, NBC was originally gonna name the show "The Hogan Family," but later changed their mind and opted for a name that reflected its original famed star "Valerie Harper." Thus, it was retitled "Valerie."
After, the famed contract dispute over her salary, Valerie Harper left the show, or was fired - depending who's side of the story you hear- thus the show was renamed "Valerie's Family: The Hogan's." This angered "Valerie Harper" very much, and she sued the producers for still using her name as the title of the show without her permission.
Thus, the producers opted to revert back to the original suggested production title: "The Hogan Family."
In reality they were always 'The Hogan Family.'
After, the famed contract dispute over her salary, Valerie Harper left the show, or was fired - depending who's side of the story you hear- thus the show was renamed "Valerie's Family: The Hogan's." This angered "Valerie Harper" very much, and she sued the producers for still using her name as the title of the show without her permission.
Thus, the producers opted to revert back to the original suggested production title: "The Hogan Family."
In reality they were always 'The Hogan Family.'