1. It puts legitimacy behind their statements. You are no longer discussing with an internet no-name weirdo, the person you are writing with has a name and face.
2. They weild authority in the field or bear respect assigned to them and are thus using it...or simply used to writing under their name due to that.
3. They're one of "I have nothing to hide" folks. And I don't mean surveilence apologists - I mean folk who have such weirdly strong ego (without being egoists. At least most of the time) that their belief in who they are is unshakeable. They tend to rawdog the world.

Some combination of the three above is most common in my perspective.

There's really no guarantee that people are using their real name and photo in most cases. People tying their presence to their work or something is different, but I generally never assume I'm talking to the person being presented to me. Some people also just don't care, don't realize there could be consequences, or they signed up when the internet was a different place (thinking twitter would be more like Facebook or MySpace where it might make some sense to use your real name).