Bitcoin’s ledger is public. Using an address rather than a legal name does not make the resulting history private. Once an address is associated with a person or service, its recorded activity can become easier to interpret. Bitcoin.org’s privacy explanation.
What an observer can inspect
An on-chain transaction exposes the outputs it spends, the outputs it creates, and their amounts. It does not contain a mandatory field declaring the real-world owner of each output. Interpreting who paid whom requires additional information or assumptions. Transaction structure.
For example, a transaction with two outputs does not label one as a merchant payment and the other as change. A plausible interpretation is not the same thing as a proven identity.
Fresh addresses help, but have limits
Reusing a receiving address makes it easy to group those receipts. Using new addresses avoids that particular repeated identifier, but does not guarantee that the transactions cannot be linked by other information.
Publishing an address alongside a name or account can create a durable association. Bitcoin.org discusses address reuse and public disclosure as privacy concerns. Address practices.
Public keys can disclose more than expected
A BIP 32 extended public key can derive descendant public keys along supported non-hardened paths. Sharing one can expose a branch of wallet activity, rather than just one payment destination. The fact that it is called “public” does not mean that publishing it has no privacy consequences. Extended public keys.
Ask what each service learns
The public chain is only one source of information. A wallet service, payment counterparty, or other service can have context about a transaction that the chain alone does not provide. Treat any claim of complete anonymity as something that needs a precise explanation of its assumptions.
To understand the objects an observer is following, continue with UTXOs. For keys and signing authority, read wallets.