Generating a new public key doesn't add data to the blockchain. Only when you sign a transaction. And if you're talking identities, as in moving around websites

Generating a new public key doesn't add data to the blockchain. Only when you sign a transaction. And if you're talking identities, as in moving around websites, there's no way to link your various public addresses (logins) unless you explicitly do so using the private key you used to generate the public address. Or, you could use the same public address. So, it depends on what you want to do. Do you want privacy? Or, do you want the site to know your activity history? The beautiful thing is, you get to choose.