Facebook prohibits creating a profile for anyone but yourself, but you can set up a Facebook page for a business, pet, imaginary person or any entity that doesn't share your real name and personal information. A page is different than a profile in that a page is meant to build an audience while a profile is meant for socializing.
Create a Facebook Page
Visit Facebook's Create a Page section to set up a page for your pet (link in Resources). Choose “Artist, Band or Public Figure,” click “Choose a Category” and select “Pet” from the menu. Enter your pet's name in the text box and click “Get Started.” The next few setup pages prompt you for account information, such as a description, photos and external site URL. If you want to advertise your page on Facebook, enter payment information when prompted.
Convert a Profile Into a Page
If you already have a Facebook profile for your pet, Facebook will consider it misclassified and has the right to delete it. Facebook recommends converting it into a page to keep the information, photos and username together without setting up a new account. To convert the profile, sign in to the account, then visit the section titled “How Do I Convert My Personal Account to a Facebook Page?” (link in Resources). Click “Start Converting” and choose a category. The account information is automatically transferred.