How To Delete Your Personal Facebook App but Keep Your Business Page
Facebook has not yet made it possible to deactivate your personal account and still keep your Business Page active. Whilst you can add different email accounts to become “Administration Roles”, the primary account is connected to the very existence of the business page.
Click the down arrow in the top right, select Settings and then Privacy. The section on “Who can see my stuff?” provides options from “Public” to “Friends” to “Only me”. You don’t need to delete your personal profile if only you can see it.