No, Bitcoin is not inherently anonymous. With Bitcoin all coin transfers between addresses happens publicly. If someone knows a particular address belongs to you they can watch the activity on it.
However, it is possible to use Bitcoin completely anonymously if precautions are taken. It's possible because you can create wallet addresses anonymously, so that people may see what happens with any given address, but not know if it's associated with you. There are ways to obscure your IP address too, like using Tor, which can make tying things to your identity difficult to impossible