This is an immigration question. I've changed the practice area in order to allow attorneys with that expertise to respond.
Be sure to click Best Answer if you found this helpful. Disclaimer: Please note that this response does not in any way an attorney-client relationship between Kathryn L. Hilbush and the recipient. My responses are general in nature. They do not constitute legal advice. You are advised to consult an attorney regarding this and any other legal matters.
If I understand correctly, your father's name is different from your grandfather's name. However your father's name on his birth certificate is not the same as his name in other documents.
It should not be such a big problem, but a simple consultation with a lawyer will help you a lot. First, the lawyer will properly formulate the question. Second, he/she will have the opportunity to take a look at the documents and tell you if proof of identity and relationship is sufficient. You may need to find/produce more documentation, if required.