You have two options:
1. Get the correction made to names in documents to match the passport. (Whatever your father's name is in hisr passport)
2. Attach an explanation letter/affidavit sworn with a lawyer or agency that does affidavit why names are written differently on record and Passport
For immigration purposes use the name in passport so whenever the there is a need all the travel documents will allign with passport. Other documents are not of importance when traveling