Is it permissible to write the name of another person on a medical prescription for patients and workers in the clinic, and what is the ruling on moving to another area due to the rejection of that?

You must adhere to not falsifying, and abandon cooperating with patients in deception and consuming people's wealth unjustly, even if this provokes people's anger, in accordance with the Almighty's saying: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression). Whoever seeks Allah's pleasure, even if it incurs people's displeasure, Allah will suffice him against the burden of people. And whoever seeks people's pleasure, even if it incurs Allah's displeasure, Allah will be displeased with him. No one among creation can stand between you and the good that Allah has decreed for you, or ward off from you the harm that Allah has decreed for you. Fear Allah in your work, and do not assist a sinner in his sin, nor an oppressor in his oppression. For whoever fears Allah, He will make for him a way out and provide for him from where he does not expect, and whoever relies upon Allah, He is sufficient for him.