Name Change Passport

I don't have last name. I want to add surname to my name. I also want to apply for passport. But the problem is they ask for 10th certificate. And I have my old name in 10th certificate. Should I change my name legally first and then apply for passport or apply for passport first with old name and then reissue the passport after changing the name. Please suggest. Will old name on 10th certificate create any problem for passport?