See I'm thinking no - don't they mean YOUR name and your DH's name? For what reason would the hospital care about your parents and your in laws? You may not technically be walking into the hospital as a parent but you will be walking out as one.
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I think they mean your name and your husband's name. That's what they wanted for my paperwork, anyway. (It's awfully redundant, considering they also wanted my name in a separate spot and they needed my husband's name all over the insurance section, but I find that medical paperwork is sort of like that.)
Re: pre-registration questions
Yes! I think so. I just sent my forms in and it is a questions that will be needed when producing your baby's birth certificate.