My sister recently went to USA for higher studies and there is no family name in her passport and in all her certificates. Her college has not accepted her application for social security number. Is family name a must for SSN and if so what she has to do?

I don't understand your question - she would apply to Social Security for a SS number, not to the College.

She would get a SSN based on the ID she presents, including her birth certificate.

My sister recently went to USA for higher studies and there is no family name in her passport and in all her certificates. Her college has not accepted her application for social security number. Is family name a must for SSN and if so what she has to do?

Like Judy, I'm confused as to what you're asking. Does your sister have a SSN or is she trying to apply for one?

Are you saying that the college denied her application because she did not have or wrote down an invalid SSN?

What do you mean by "family name"? Are you referring to her last name? How was she able to obtain a passport without providing her full name?

Yes, she needs to provide her family name. The passport can be issued out by the home country with only one name, generally to be considered the family name, as is common in some countries. Please note the CONOFF generally will not issue a visa unless it is annotated. FNU or NMI.