There are no anonymous bloggers, because a blog has an identity after awhile. It has a character. And that's your pseudonym, even if you don't have a screen name. Before I had raincoaster.com, I had a blog called Terminal City, and there I was still raincoaster, but there are lots of people whose usernames are their blog names. The blog name then becomes their pseudonym.
Anonymity is the condition of not having an identity. Pseudonymity is the condition of having an identity independent of your official name and in most cases (not all, as in my example) having the official name hidden from view, disconnected entirely.
There are anonymous people on the internet; commenters who don't have usernames, lurkers, etc, but without the willingness to put a piece of your character out there, you can have only the most transient of effects. A mask is both freeing and powerful: I used to collect a list of cool screen names, and it was very interesting reading. People tell you things about themselves just with their names.
Some people try to blog without putting any of their character or opinions into their blogs, so they don't give away any clues to their identity. But if you don't give any clues to your character your blog will die; I've seen it a hundred times. Not even the blogger can stand to read it, and it dies within three months.
Truman Capote said that women who choose to become blonde are blonder than those who were just born that way. It's the same with choosing a name.