Bitcoin is perfectly pseudonymous and traceable. Which means, if you don't mix transactions between your different identities, you can preserve your anonymity.
Say, you made some coins by selling your coding skills (or naked pictures) online, without revealing any personal information (IP and personal e-mail addresses included). Then you went and spent those coins to pay someone to build your anonymous identity a website. This is perfectly doable.
However, if you then go and order some pizza to your home address with the rest of those coins, it is possible in theory for an entity with reach to associate your code (or naked pictures) to your home address.
It also works the other way. If you buy some coins with a bank transfer, it's possible that they can associate your expenditures with your ID. There is plausible deniability of course, but that won't prevent them from breaking into and searching your house when you are away. If you are perfectly sure that the people you are transacting with are not agents, you are likely safe.
Luckily, since there is very limited friction, it's fairly easy to figure out how to cover your tracks. Required learning is similar to what you have to do for WWW or e-mail (which everyone needs to know at this point anyway). If you are familiar with the innards of historical digital currencies, you already know.