Honestly I think the answer is a depressing no. Your face is already on some facial recognition software somewhere (most likely). If you pay for an internet connection, your IP will be able to get traced back to your real world identity. If you have a cell phone or use a modern computer, there is so much finger printing and tracking going on that its basically a lost cause.

Now there are steps you can take to fight for your privacy, but if you take part in the modern world, I don't think there are any easy steps. The acronym boys have access to all the identifying systems and much more.

Now if you are serious about guarding your privacy, there are steps to take and a more privacy focused forum/board/community can give better pointers than me, but if you are looking to not be identifiable or untraceable by a state actors, that's some real spy level shit. Remember "they" can find and identify the serious cyber criminal players, but most of the time these guys are in countries that dont have extraditions to the US. An anonymous cyber criminal only has to fuck up once to be uncovered