Sophitia is most likely a name derived from the greek name Sophia, which means wisdom.
Wis-dom: 'the ability to make sensible decisions and give good advice because of the experience and knowledge that you have.' Accordong to Oxford Dictionary.

There is no doubt that this name suits her! Sophitia is a woman of great wisdom, being so close to gods she knows when she must fight (as she says: "It is because I am a mother, that I fight for my children's future") and when she should stop. She's been through a lot so she certainly can give good advice ("Leave at once, it's for you own good"), based on her personal experience with Soul Edge.

Her last name Alexandra is Greek as well, of course, and it is the female version of the name "Alexandros/Alexander". Alexander was the king of Macedonia (north part of Greece) during the 4th century. He won great battles and extended the borders of his Kingdom to the East and Egypt.