Not really. Bitcoin might seem anonymous initially, but this isn’t correct. The Bitcoin blockchain is public and anyone can see the transactions. Your identity isn’t tied to your wallet addresses on the blockchain, but an observer with the right resources could potentially link the two together. It’s more accurate to describe Bitcoin as pseudonymous. Bitcoin addresses are viewable to everybody, but the names of their owners are not.
That said, the system is relatively private, and there are methods to make it even harder for observers to figure out what you’re doing with your bitcoins. Freely available technologies can create plausible deniability to “break the link” between addresses. What’s more, future upgrades could massively boost privacy – see An Introduction to Confidential Transactions for an example.