In German law there is the possibility of Einbenennung.
Example:
Miss Born marries Mister Adam, and they take the name Adam for the couple and all children.
They get the son Anton Adam.
The father dies and the widow marries Mr. Chester.
If Anton Adam gets the name Anton Chester after his stepfather without adoption, then he is "einbenannt". This is "Einbenennung".
What are best English words for "Einbenennung" and "einbenannt"?