No Surname in passport India

I am Vikas, and I am from India. My passport only has the name ‘Vikas’ and the surname field is blank. If I add my surname through a gazette notification or by updating my Aadhaar card and PAN card, do I also need to update my surname on my 10th, 12th, and degree mark sheets? Without changing the surname on my mark sheets, can I still get admission for an MS program or a visa?

Aadhar, PAN, 10th, inter etc are only applicable within India. Passport is the source of the truth for your identity and permissions to get any approvals(including travel) across the globe.
Having said that, first get the passport updated with your last name in India before attempting any other international travel things.
A way to look at it is, declare a self affidavit and get all domestic documents updated (start with Aadhar, then PAN, your bank statements etc). Then use these to get your passport updated. Once you have it in hand, from that point onwards, your name is one and only what is on your passport. If you dont have this fixed, you will run into many complexities down the line.