inventing a new name for yourself can be rather difficult; yes, you can always change an internet alias to something new later, but once people know you by something it tends to stick no matter how hard you try.
the first thing to worry about is finding something you like; then follows the problem of making sure nobody else has already registered it on your favorite instant messenger or e-mail. usually, no matter what you come up with nowadays, it will likely need to be altered somehow; for example the alias "bug" would very likely be registered and therefore need to be changed to "bug byte" or "bug72280" or something along those lines. the simpler it is, the less likely it is that you're going to get it, unless you steal it by cracking their password, but that's not nice.
one thing that bugs me is all of these independent websites out there requiring you to register a unique account for that particular site. i must have a hundred or so different usernames and passwords, some of which i don't even use. some noobs (people new to computers) actually believe that when you register an account with your isp (internet service provider) that it allows you full access to everything else but unfortunately it doesn't work that way. so be forewarned, if you're an active internet surfer you'll be registering new accounts all of the time. it is a good idea to create some sort of standard for yourself so that you don't get lost, by having similar usernames and passwords unless it's for an important account. it's also a good idea to have a junk e-mail address for this amongst other reasons.
an alias is an important thing; it can say a lot about you, whether a childhood nickname or just something that sounds neat to you. personally, i like to think of creating aliases in the same way that the american indians named people in their tribes. i believe an alias should describe an individual's personality or something unique about that person that can usually only be deciphered through explanation. take my name for example: tapeworm, worm, or tapeworm byte depending on how many syllables i feel like pronouncing. this wasn't my first choice, or even the one i liked best; it just happened to be the one that stuck. as disgusting as it probably sounds, tapeworm came about because of my fear of doctors, and the fact that i'm extremely skinny. i hadn't been to a doctor in so long that somebody once commented "how do you know you don't have a tapeworm or something?" to which i replied "i don't know." then jokes starting coming, for example when i was hungry i wouldn't just be eating i'd be feeding my tapeworm :-) isn't that cute? the "byte" was added because tapeworm itself is a very popular and commonly used name, plus it's a play on words as it sounds like "bite" but refers to a computer "byte" if that wasn't obvious. it was never really intended to sound computer-infectious although that has worked to my advantage.
you should spend a good amount of time inventing a name for yourself; it will be everyone's first impression of you. it also extremely critical that you demand all of your friends irl (in real life) refer to you by your alias, never respond to your birth name unless you're at work or in front of family. if it helps, an internet alias is generally between 613 characters long.