The only ways to not be embarrassed by what is online about you are. [And I understand embarrassment is not the only reason to be anonymous, but if people are honest with themselves it is 90% of the reason they care.]
1. don't give a shit / don't be embarrassed / don't live by other's standards or norms (this seems easiest to me but I'm sort of anti-social amoral and have not been giving a shit what others values as they apply to me from a young age, YMMV)
2. Don't do embarrassing things. Sort of corollary of #1 (as in the less you are embarrassed by the easier it is to not to embarrassing things.
3. Don't live in modern society. Get born some place with no electricity and kill (optionally eat) all the scientist who come to study/photograph you.