Steam is very unclear about account removal. You should try to file a removal request using the contact form found here: http://store.steampowered.com/ssa_feedback since your account cannot officially be deleted by request. On their support pages they state: 'Only inactive accounts containing no games are deleted. Accounts cannot be deleted by request.' However, one of our visitors pointed out that some removal requests are in fact granted, so it's worth the try.
A new name can be registered if for some reason you need a new account. For more info on cleaning up your computer from all Steam-related data see: http://answers.yahoo.com/question/index?qid=20070913044038AAQrc8N
Then, the Subscriber agreement of Steam states that you can always cancel your account (but how?!). See: http://store.steampowered.com/subscriber_agreement/
Concluding: it seems nearly impossible to delete your account, since it can never be done by yourself, except for 'deleting all your games from your account first, hoping for the account itself to be deleted'. Probably this will be done automatically since then your account will look obsolete.
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks you can always contact Steam and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for Steam using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Steam. Click the icon below to find out how.