How to write a letter to bank manager for wrong name?

Using a standard business letter format (link below), state the problem and any specifications as your first paragraph, 'I am writing to advise you..., and to request...'

Use the second paragraph to explain the problem and the reasons (s) for the request, keeping it short and to the point. Mention or list anything that may be attached to support your request.

Start the third paragraph with any important dates or time frame, if applicable; next provide the information necessary for them to contact you; and the last sentence is used to thank them for their time and/or their action.

That's all you need.