Regarding surname

My name is Sreenath, and I don't have a surname on any of my documents. I want to add my father's name as my surname, as it's required for my passport application. However, they're asking for my 10th standard certificate, which is from CBSE. I visited the municipal office to add my surname on my birth certificate, but they said they can only do so based on my 10th certificate. I emailed the CBSE regional office in Trivandrum, and they replied with a procedure that involves visiting my school and applying from there. But when I went to the school, they told me they can only send a request to the CBSE office if my birth certificate is changed. I'm stuck in a loop. I need to change my CBSE certificate first, followed by my 12th, degree, and PG certificates, as well as all my other documents. My main goal is to add my surname to my passport. Is there an easier way to do this? Even if I can't change all my certificates, I at least need to update my passport, as many countries no longer accept people without a surname.