No, it's built to be pseudonymous, but it's very difficult to keep transactions pseudonymous because many people have revealed some kind of identifying information about themselves in connection with their address on the Internet.  Especially with exchanges that have KYC in place, governments and others can draw connections between known Bitcoin users and the people that they are sending Bitcoin to.

Satoshi did not claim that Bitcoin is an anonymous system, rather that the possibility to be anonymous or pseudonymous relies on you not revealing any identifying information about yourself in connection to the Bitcoin address you use.