If there is a spelling error or mix up of your name, you'll need to request for the errant party to update their records with your correct name.
If the letter is being sent as a hard copy, then it should be in the proper business format, otherwise, if the letter is being emailed, it should have an appropriate subject line and proper grammar.
I am writing to request that you update your records to correct my name. The name that you have on file for me is John Smith but my legal name is Jon Smith (without an "h"). For your reference, my billing number is C65486. I have enclosed a copy of my drivers license as proof of my correct name.
If you have any questions, you can reach me at my cell at 555-555-5555.