Sure it is possible. You must remember though, especially in the beginning - depending of your behavior and presentation - anonymity comes with the cost of others possibly not treating you as a serious aspiring professional. Given that it is what you are looking for.
In the long run a successful anonymity can be good, especially in the indie world. You can create a persona around it that is completely separate of who you actually are. It comes with challenges once you begin gathering followers and supporters around you. Being anonymous might become very lonely unless you have a group of others who want to be anonymous.
I know I might think far ahead but your goals in the end determine whether it is good to be anonymous or not. If yes, in what degree? If no, why not?
Personally I prefer interacting with my actual identity with the people I work with. I miss real people and it gives an extra "demand" for professional behavior.