When we study the early Church, we see Christ's followers renouncing their former allegiance to the state and giving their loyalty to the living Kingdom of Jesus. They refused to register with Caesar and had nothing that belonged to Caesar. Therefore, they did not obligate themselves to render back to Caesar.
One little thing we can do that is a thorn in Caesar's side, is to forsake our state name and obtain a name from Heaven. Our new name is created by God, not the state. Therefore, we are obligated to render back to God that which is His.
We only have an obligation to obey Caesar when we are one with Caesar. If we belong to Another, it is none of Caesar's business what our name is.