All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is unlawful to forge documents. It is impermissible to do so unless there is a compelling necessity; and whoever does so with no legitimate excuse is sinful, and repentance from it becomes due upon him by regretting his sin, abandoning it, and changing the matter to its reality, and correcting his name, so long as this will not lead to more harm.
As regards your father’s job, then there is no harm in doing it as long as he is competent to do it and performs it as required. There is also no blame on you to benefit from what he gives you out of the salary he takes in return for his permissible work.
On the other hand, changing your name in order to join your father is impermissible unless you are compelled to do so by necessity considerable under Sharee‘ah; Allaah The Almighty Says (what means): {He has explained in detail to you what He has forbidden you, excepting that to which you are compelled.}[Quran 6:119]
For more details, please refer to Fataawa 87821, 92226 and 86193.
Allaah Knows best.