It sounds to me as if they are trying to give the baby status, since they no longer have it. It has nothing to do with gaining favor. They are stealing status for the girl to carry thru her life. And it is a great social conversation for their new friends.
It wouldn’t have surprised me if they’d named the girl ‘Princess’ as her first name....just to make a silly point.
Elizabeth's name of affection amongst her closest loved ones will be trashed and dragged through the tabloids for the rest of the child's life. Just wait until she gets to school, and starts to be called "Lilibutt" and "Liliwhite" by the other kids.