Then, keep a separate Chrome profile that's logged into the fake facebook, and your identity is safe. Probably best to lock down all privacy settings on the fake user to absolute maximum lockdown, to avoid information leaking onto Facebook's public layer that may tie you to it.
That was the strategy I used when I worked for a company that did business with Facebook games. Those things were so spammy, I would never want my actual friends to be spammed with all the viral content. To this day I keep my fake account for any and all untrusted FB-related things.
I recently wanted to create an "Admin" account for a client I was developing a web-app for as I didn't want to link my personal facebook account to my work. But with the phone number requirement the account got flagged and rejected from the system.
Frustrating!