The bank name should not matter as long as you entered the right routing number, account number and whether it was a checking or savings account.
If your account number or routing number was wrong, and the IRS accepts your E-Filed income tax return, the IRS will send you a check in the mail. See What if I entered the wrong bank account for direct deposit?
If you entered any other information, wrong:
And you already E-Filed it, you would have to wait and see if
your return was accepted or rejected.
If the IRS rejects your E-Filed income tax
return, you could change your information.
If the IRS accepts your E-Filed income tax return, see How to Amend (Change or Correct) a Return You Already Filed to
amend your income tax return. Please keep checking the TurboTax FAQ for the
status of amended return tax forms.