I am not sure how the popular implementations address this, but generally speaking you can add arbitrary additional plaintext to each transaction in the block,

I am not sure how the popular implementations address this, but generally speaking you can add arbitrary additional plaintext to each transaction in the block, and contribute that extra data to the signature with the private key. For example, full name or social security number (not applicable in the US since socials are private info, but feasible in asymmetric key ID systems such as Estonia's. Which brings up another potential application of blockchain: identity verification and management).