How can I correct my bank name with the IRS after e-filing my tax. I owe taxes but entered one bank name and different bank account number? Number is correct

If you have already filed your return and it has been accepted by the IRS for processing, you won’t be able to change it. You need to contact the IRS to try to expedite this process. They will put a hold on the direct deposit and issue a paper check instead. 

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What if I entered the wrong bank account for direct deposit?

As long as the routing number and the account number is correct, the bank name is not really relevant.