That's not how Facebook Pages work - a Page isn't an account you log into, it's something your main Facebook account can have admin rights to (and a Page can have multiple administrators). I have admin rights on a few Facebook Pages but I only count as a single active user, and I don't have to log out of my Gregor account to administer them.
Historically, some brands did create full Facebook accounts, but Facebook now discourages that and as far as I know most brands are using Pages now. For a while Zuck's dog, Beast, was a notable exception (he had a Facebook account long after that was discouraged) but it looks like he's just got a Page now.
I don't recall Beast ever having anything but a Page - in fact, I remember that Zuck mentioning in a Q&A that he was using Beast to get a better feeling about what it's like to run a Page.
Historically, some brands did create full Facebook accounts, but Facebook now discourages that and as far as I know most brands are using Pages now. For a while Zuck's dog, Beast, was a notable exception (he had a Facebook account long after that was discouraged) but it looks like he's just got a Page now.
(I used to work at Facebook.)