Sophia comes directly from the Greek word for wisdom, and it's traditionally associated with clarity of thought rather than mere cleverness -- the kind of wisdom that comes from experience, not just intelligence. Names built on this root often carry an expectation of quiet authority, someone whose judgment people trust without her needing to assert it.
We ought not to use arguments or tedious discourses in giving judgement, much less flatteries, but only to pronounce what is known by experience and firm reason. - Cardan Girolamo (1501-1576)