Why Chris children has not taken his last name or is it because his wife is the head of the Childe family?
Yes. Wife is the head of Childe's house and the children will be taking the head position after the wife. And most importantly Chris is the second son so it is better if the children take her name rather than his. They will have some power.
Oh thanks for answering
Why Chris children has not taken his last name or is it because his wife is the head of the Childe family?