Owl You could be an influential or aspiring politician, a public figure, afraid that opponents/rivals might somehow use your communication for smear campaigns. Or you could simply want to be more discrete, keeping more control over what information about you is circulating around.
then simply use a synonym or a false name. Angelina is my real name, but can I prove it? No!. I admit it's tricky, but on the internet we leave our traces all day long. If you want to be anonymous, don't use the internet at all.