How do hackers find account usernames?

Just curious, and wondering if anyone knows about this:

How do hackers find out the user-names of registered users?

One of our user accounts has a unique and not-obvious user name; it contains letters and numbers in an non-intuitive pattern. Login Security Solutions notified me that an attacker was trying to gain admittance using that user-name. It seems unlikely that they randomly guessed that user-name. How do they get a hold of them? What are some of the ways they can ‘learn’ user names?

Related question: are user names case-insensitive?