My parents were often socially discriminated?

A degree doesn't make you any better or worse than anybody else so people that think so should be avoided

If ppl discriminated your parents, that is their terrible problem and not yours. Don't make others force you do something so drastic like changing your name. You can be successful without a degree. Being hardworking, honest, and a decent person is more important. Don't be ashamed but proud of who you are and your parents.

Those three facts are completely unconnected. 

Your question makes as much sense as if you’d asked “My parents smelled of elderberries. I’ve just become the first vegetarian in my family. Should I buy a new house?”

What happened to your parents is now irrelevant. Good luck with your studies, and do as you wish with your surname whatever result you get in your finals.

It's not necessary to change your name.