Name change and related questions

[prisrose]

I got married last year and as my passport was expiring this year, I waited to change my name from maiden to married and do it in the new passport upon renewal.
I got my new passport now with the new name to it (changed last name). However, this has caused some anxiety as I have a few questions about the impact of this name change. Only (Identification) document that I have now is the passport. Please help me in these areas-

1. My US Visa is in the old passport. Also, all other documents like I-797 and I-94 has my previous name. How do I change them? Each of the document needs name change?
2. I have plans to travel this June-July to India. Will I have difficulty entering in as my name would be different in Visa and new passport and other documents?
3. Do I have to go through the name change process- advertise in the newspaper etc (as how we do in India for name change?)? Please help me in this area. I am confused about the process.
3. The new name has to be in my drivers license, SS card, and other bills. Do I change each of them individually?

I need some insight in this process. Please help!

Thanks!

Pris