it is illegal to have a different surname for a newborn child that is different from his/her father's?
They won't register your kid under a different surname from his father's surname.
And without registration the kid will get no facilities from the state.
So there is no question of legality.
I know at least one hindu who doesn't have any surname.
It is pretty common custom in South Indian states to not use surnames.
They usually stick to just first names or first name and fathers name, and in certain cases if they are compelled to use a last name they use their village name of the name of their house.
eg. PT Usha or P Chidambaram.
i personally know have secular surnames which dont indicate any specific religion...what about such cases?
In that case that person is one lucky guy and will probably never be directly discriminated against.
But then again, the Old Indian uncles are never too shy to directly ask to your face "Which caste do you belong to?" They will always try to justify it in some of the other sense but some of them are shameless enough to ask you that directly with a stone cold face.