Sunname - Problem

Hi Sir, I am from Tamil Nadu. We don't have surname in our culture. We are using initial naming system. For ex: My name is Arul Johnson Raj L, My dad's name first letter will be used as initial. My dad's name is Louis. All my academic certificates will be having the name is Arul Johnson Raj L. But in passport We need to fill surname, So We were expanding our initial as surname like Louis. And for my son, I am going to take passport. My son name is Jerish, and I need to fill my name as surname in passport, So his full name will be Jerish Arul Johnson Raj. This will create lots of trouble for him due to lengthy name. So my concern, is there any possibility that can I use Johnson as surname for my Son's passport? So his full name will be Jerish Johnson. So it is easy for his life. Please suggest. So here after my next generation can follow Johnson as surname... Do We need to submit any proof for this? And also in birth certificate there is no column for adding su rname in my local office. So We got a name registered as Jerish.