does my last name will change?

Depends on what was written in the birth certificate when you were born. What was written in there is never changed by NSO. they only archived what was written in the original birth certificate. so if you have the original one most probably it is what you will get at NSO.

It wont change. You are being recognized by your father even your mother and your father are not married. It was already written at your name and your father's last name as your last name. If your father did not recornize you as his child then your mother's last name will be used. But in your case, whenever you will get your birth certificate at NSO, your father's last name is your last name too. It was being processed as soon as you were given birth by your mother at the hospital or your place of birth. I hope I helped you.