Spencer is a name that has everything: it's both distinguished sounding and accessible, dignified but Spencer Tracy-like friendly. Picked by several celebrities (a couple of times even for a girl), adding up to an enthusiastically recommended choice.
As a family surname, Spencer became the middle name of Winston Churchill, and was the maiden name of Princess Diana. The surname version was often spelled Spenser in the past, as in Edmund Spenser, the poet known for The Faerie Queene.
Yes, Spencer makes a plausible and powerful female choice these days, though still thought of as primarily for boys. Kelsey Grammer used it for his daughter in the 1980’s.