A long time ago, back when your "lighting-fast" 300-baud modem could fill your 24x40 character screen in under 30 seconds, a lot more people in what eventually came to known as the cyberspace used their real names. It started out because most users where connecting through professional institutions and their accounts were created from their student / employee files. This lasted through the 1980s, when most hobbyists connected through
dial-up BBS'es that were local and people knew each-other IRL (in real life), but was already starting to fade out, and disappeared with the popularization of online games and
chatting with dogs.
As using your real name in your online identity became less frequent, it became more of a deliberate social statement.A quote from the
C2 (Web's oldest real wiki)
RealNamesPlease page, which became a meme-name for this concept: "In general, it is observed that people who use online nicknames care less about what they write.
The discussion is usually taken more seriously when people do not use NickNames, but use their real names."
In the political context, I believe it also shows dignity and desire for constancy in your convictions. It's one thing to argue for decriminalization of marijuana or kiddy porn while hiding behind an alias (an illusion of anonymity that the government can see through in vast majority of cases), and it's a completely different matter when you're using your real name, that your past acquaintances, relatives, and future employers are likely to Google.
It lets people know you're not just having a one-night-stand with this philosophy, you are married to it. It tells people: "Here I stand, and I don't want to do business with anyone who wouldn't want to do business with me after Googling my name."
In my opinion, this shows courage and integrity.