facebook are asserting a right to prevent other people using the word "face" in particular ways.
In comparison, copyright is a right to prevent other people using particular words, pictures, sounds, etc, in particular ways. If copyright is "ownership" then so are trademarks too. Furthermore, trademarks can be bought and sold, another indication that they are a form of property.
So, yes, it isn't too much of a stretch to say that facebook are claiming a (limited) form of ownership over the word "face".
Trademark is saying that a particular look, feel, phrase or whatnot normally represents the company or organization and as such it is owned by the company as an identity. It's the exact same thing as your personal signature, which I'm sure you have a vested interest in.
Copyright is a creation of something new, (or the idea of the intent to create something) that says you aren't allowed to use it period unless you ask for the creator's permission, since it isn't yours. This include copying it exactly.
Incidentally, protecting trademarks is a social program for business. Proponents of smaller government and libertarian ideals seem not to want the government to get out of the trademark business.
facebook are asserting a right to prevent other people using the word "face" in particular ways.
In comparison, copyright is a right to prevent other people using particular words, pictures, sounds, etc, in particular ways. If copyright is "ownership" then so are trademarks too. Furthermore, trademarks can be bought and sold, another indication that they are a form of property.
So, yes, it isn't too much of a stretch to say that facebook are claiming a (limited) form of ownership over the word "face".