Different spelling between father's given name and child's s

Is there any rule in India governing the use of father's given name as child's surname? In all documents of mine, my name is Mirsa Mohammed and my father's name is P M Mohammed. But in my father's documents his name is P M Muhammed. (Notice the difference in spelling 'o' instead of 'u'). I want to keep in sync my documents with my father's documents. For that I'm trying to understand is it enough to correct father's name in my documents to use 'u' instead of 'o' and can I keep my surname unchanged? Means after the change in my documents can i have my name as Mirsa Mohammed and my father's name as P M Muhammed? Thanks in advance.