In the history of the site we have had several users with the moniker "Anonymous". Likewise I know we've had at least three "Atheist". Most of these have at one point or another given up on the handle and resorted to other aliases.
The SE user system does not guarantee unique user names. This is pretty much a free text string. There is, for example, another high rep user on some sites that I use named "Caleb". You will even find our posts and comments side by side in a few places. Comments in particular are difficult to follow.
For posts, the user card almost always shows a gravatar. This is either a user supplied image or a special geometric pattern developed based on the users supplied email address. Since two different users aren't going to have the same email address, no two gravatars are likely to be alike. This is the basic way to tell them apart. In the case your your Anonymous, he has a very distinctive gravatar.
In some rare cases, (notably when people get carried away over on M.SO or when servers are too well behaved for two long over at ServerFault) you will see multiple users deliberately using the same gravatar. This is, well, just silly and stupid. Now you know what I think of that. Thankfully most of the historic culprits have come back to their senses (and their regular gravatars).