Your identity will not be revealed as you don't make any KYC on gambling sites.
The address can be monitored, but not you, it's only revealed the moment you will exchange your bitcoin to an exchange as its easy to determine your name and the source of the bitcoin you are transferring from.We can call this mixing but it's useless if you will not sell your bitcoin to an exchange where your identity will be revealed.
So if you are asking if, would the authorities know I'm gambling?
Yes, because they can track the wallet of a gambling site whether regulated or not.