Partially. Your bookmaker knows that it is you who handles the betting activity in your account. However, the system cannot know where you send the money once you withdraw your winnings. Bitcoin transfers are executed as encrypted data. The sender doesn’t know where the money goes. Likewise, the receiver doesn’t have any idea where the money comes from. The action of transferring money is known by your bookmaker and your blockchain wallet. However, that is all the info that they have. Since only your bookmaker knows about your betting activity, which it should, you stay as anonymous as possible.