It's strange ... in casual English it's quite normal to use "they" or "them" to designate one person of unknown gender, but that doesn't sound right in this case.

Compare "When you meet somebody for the first time, be sure to learn their name" to "When your baby is born, you'll know what their name should be."

To me the first sentence sounds normal and the second quite odd; it would seem more natural to use "its".

I wonder why that is.

Marion