ANSWER:

No need to refuse the proposal if the girl is righteous. After the marriage she should try to change the name officially and meanwhile, she should only be called after Abdurahman. 

QUESTION: A marriage proposal is going on. the girl’s father’s name contains the word ‘Rahman’ without abdul. If they don’t want to or refuse to change it should I refuse the proposal even if she is righteous? because father’s name is obligatory to write in the marriage registry in our country. Will the sin of shirk be upon me If this name is on my marriage registry?