What is the meaning of the names "Hajar" and "Sarah" so that I may choose one of them for a new baby girl, knowing that our mother Hajar was a bondwoman to Sarah?

Naming a newborn is the father's right in case of dispute, based on the Almighty's saying: "Call them by [the names of] their fathers; it is more just in the sight of Allah." Therefore, your husband has the right to choose a name for his daughter. The name "Hajar" does not necessarily mean "emigration," and it is permissible to name a child "Hajar," just as it is permissible to name a child "Sarah."