Is it an issue if I put the wrong bank name for my refund? I put the correct routing and account number but I put the wrong bank name.

No, that is not an issue providing the routing number and the account number are correct for the direct deposit.

The routing number and account number are what matter.   The IRS is not looking at the bank name.  If you have those right, it should be okay.

If you mess up the routing number or account number----then you have a problem.

You cannot  change banking information while your return is in pending, nor can you change it after the return is accepted.  The IRS does not allow it.

If you e-filed:

Banking information for direct deposit is wrong or closed

If you entered incorrect banking information for your refund, you can change it if your return is rejected.  If it is accepted, however, it is too late to change it.  The bank will reject the refund and send it back to the IRS.  Then the IRS will issue a paper check and mail it to the address you put on your tax return.  Expect a delay of at least a couple of weeks to receive your refund.

Here is what the IRS says about entering incorrect banking information

https://www.irs.gov/help-resources/tools-faqs/faqs-for-individuals/frequently-asked-tax-questions-answers/irs-procedures/refund-inquiries/refund-inquiries-18

Probably won’t be a problem but if it is you will be sent a check. 

I did the exact same thing, so did you still receive it even though you entered wrong bank name, was it an issue or did it affect your tax return deposit??