I am new to bitcoin and would like some clarification on its anonymity. Example: i buy bitcoins from an exchange and send them to my bitcoin wallet. The addresss that i sent the bitcoins to would be linked to my real identity, i get that part, but what if i create a new address? Or create an entirely new wallet? Would that address in any way be linked to me? Currently it seems to me that the only way to be anonymous, is to buy bitcoins themselves anonymously. Thank you
your identity can be linked to bitcoins in more ways: exchange site can gather info about you (your IP address, ID, bank account, etc), your transactions are public through blockchain, your IP can get registered when you send BTC, your IP address can be registered when you visit BTC forums or any website/honeypot related to darknet markets (illegal activities connected to BTC)... so, there are many techiques to get your identity, thetefore, you should pritect yourself by buying BTC face to face or pay someone to do it for you, and use tor to receive/send bitcoins.
It can be linked to you if you send coins to the new address that were once on the exchange under your account. This is because the entire history of transactions is publicly available and the coins that were once in your account can be traced*. An understanding of transaction inputs and outputs might also clarify, see Transaction - Bitcoin Wiki
*Now, there are ways of anonymizing, Coinjoin is one example, so that it is difficult to follow the trail of coins who's owner was once identified.