Medical Bill

Howdy! I have a ED bill for my daughter from the university of utah. I am listed as the "bill to" person, but my daughter's name on the bill is no where close to her name. "Lwat C." Is the first name and middle initial on the bill. Middle initial is wrong and the first name is not even close. She has an account at the U with her correct name. I don't know why they didn't use this account. Insurance obviously covered nothing as the name doesn't match at all. I called the hospital billing about this and they told me that I need to submit her birth certificate to them in order for them to update the name and merge the two accounts. My question is, what are my obligations here? Can I turn around and ask them to prove that it was my daughter that they are billing me for? DOB matches, and last name, but that is all that matches on this bill. I really don't mind paying the bill, but the fact that they messed up and now want me to do this work to get the name updated kinda pisses me off.
Edit for more context: Daughter was 1 year old when this happened. We did actually go to the ED. The other account I mentioned is the "facility" bill. This was billed under her correct name as the patient, sent to insurance, paid for, etc. This second one under the wrong name is the "doctor" bill for the same date, and different/additional charges.
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