Is there a way we can find the name of the bank from the details that we get after scanning a card?
The only relevant info seems to be Card type - Visa etc and the last four digits of the account number.
Yes, you can. We had to do this a while back for an e-commerce application we wrote.
The first 6 digits of a credit card is known as the Bank Identification Number (or BIN). Some credit card processing gateways can return this information, or you can do it yourself. There are public databases with this information stored for each card type: VISA, MasterCard, AMEX, etc.
This list shows some of the common BINs:
And this link explains this concept to a little better depth.
Hope this helps!