Posted to 'privacy' community: "Put your first and last name on this petition!"
I expect if there are too many fake names it would be used against them too. I think not signing at all is overall less detrimental my own privacy. However if there's evidence/reasoning otherwise please share!
Edit: I ended up signing with my real name, I don't see employers or anyone holding that petition against me if they find out I signed this by searching my name.
Privacy is not anonymity in the same way as animals are not dogs. To give away anonymity is to give away a form of privacy.