This plan isn't thought through to its conclusion. If a government is willing to illegally detail political dissidents, etc. they will certainly not mind lying about that dissident's decision for anonymity.
Not like the KGB of old would tell a reporter the truth when they ask if the nameless detained man in a gulag somewhere requested his name be reported and let them blow open the fact that the government is arresting non-criminals for political purposes. I mean in that situation, Soviets already knew--it's not a perfect analogy. They'll just say he exercised his right to privacy.
It only works if the announcement of identity is public by default, unfortunately. Neither option is great at all, but I don't think I'm qualified to come up with a better plan.