Recently I've been talking to one of our members (via PM) about how they want the parent's names to be listed on a child's birth certificate (this isn't about whether an individual is listed as mother, father, parent, etc., but whether they put the old vs. new name down). This member thought the nurses meant they wanted his original name no matter what (ETA: unless the original BC is "impounded"), and my personal research indicates otherwise. In most states that does apply if you've only changed your name for marriage-related reasons (here that also means civil unions, other partnerships, etc.) since having a mother list her maiden as opposed to her married last name (which is usually the same as the father's) provides more identifying information; however if you've changed your name for a non-marriage-related reason then that does change the name which would go on a future child's birth certificate in the majority of cases.
For those who have had children during or after their transition process, what's your experience with this? (Please be sure and mention what state your case was in.)
I think the reason for the confusion with the member I've been PMing is his children were born before he legally changed his name (although he had plans to do so but had done nothing official at that point), and although I haven't found much anything official I think most states will not amend another party's (i.e. your child's as opposed to your own) birth certificate due to your name change (except for information that was incorrect at the time the child was born). He probably confused that as to what you'd put down for a child born after you legally changed your name. (If his logic was correct that your name at birth goes down regardless than that means anyone who was adopted as a child, or had a "placeholder" name like "Baby" listed on their original birth certificate, would have to put a name down that they haven't used much if at all in their life.)
Also, what I said in the first paragraph appears to apply to the majority of U.S. States; there are some outliers I noticed (e.g. one wants the mother's name as it is on her birth certificate, which means a legal name change wouldn't change what she'd put down unless her own birth certificate got amended as a result).