How to change name and surname in 10th certificate

Dear sir/Madam, Good evening, I have to know how I make correction in my 10th certificate with date of birth & add surname in certificate. But my previous school pricincipal told me we are responsible for any mistake in certificate and I will not give a letter for change date of birth and adding sirname but we have a date of birth certificate for proof. But we receive the date of birth certificate after finish the10th class. So please suggest me what I will do. Thanks & regards