Is it permissible to change one's profession in official documents to something other than what it is in reality, in order to avert the harm of being prevented from practicing trade?

The state is not permitted to prohibit trade unless there is a significant interest, such as regulating the work of a specific group. If such an interest exists, adherence to the prohibition becomes obligatory. As for misleading entities, it is permissible to use ma'areed (ambiguous statements) out of necessity, without outright lying.