Is it permissible to name a girl "Amatullah" (female servant of God), and is it permissible to call her "Amah" (female servant)?

There is no harm in naming a girl "Amatullah" (slave of Allah) and a boy "Abdullah" (slave of Allah). When calling out, it is better to use the full name "Amatullah," and there is no legal impediment to using only "Amah."