All that can be found out about the transaction during its execution is the wallet number. Moreover, all transactions are open for viewing in the blockchain. How much and when the money went - this information is publicly available. But from whom and to whom, only two participants in the procedure are known.
I note that this plus is relative. On the one hand, anonymity is great: no one pries into your financial affairs. On the other hand, this is the reason for the increased attention paid to cryptocurrency transactions by the state.
If one day governments decide that digital currency undermines state security (for example, it encourages trade in arms and prohibited substances), anonymity will be a weighty argument against bitcoins.