I put the wrong bank name but the correct routing and account number. Will affect the time it will take to get my refund back. If so can the name of the bank be changed?

No. As long as the routing and account number is correct than you should be fine.

Did you get funds as expected? Currently experiencing this.

According to the IRS website, only the routing number and account number are needed for direct deposit.  As long as these are correct, you should not have an issue with receiving your direct deposit.

Reference:  https://www.irs.gov/refunds/get-your-refund-faster-tell-irs-to-direct-deposit-your-refund-to-one-two-or-three-accounts

Did it affect you at all? 

As noted above, your bank is identified by the routing number, so as long as your account and routing number are correct, you should not have a problem receiving your deposit. The IRS knows the name of the bank based on the routing number.