No, it does not. It was NOT named anything connected to wisdom when it was built as the first church and even the second. Emperor Justinian had a lot of expansionism everywhere and his aspiration were huge, therefore the third Church built in the VI century ( a LOOOONG time after Byzantine empire became Christian) and it was decidedly the patriarchal cathedral for the Byzantine Patriarch - so your stories about some obscure myth from who knows when to be the reason of the naming the Patriarchal Cathedral by the most powerful Empire of the times, which was in constant rival struggle with Rome for the official primacy of the Seat of Peter is simply laughable.
And proves you simply do not know anything about the history of that times.
I was referring to the Solstice-cum-Christmas canard -- the last line in the post. I guess you concede that.
But as to the other - sorry but the cult of Sophia long predates Christianism:
>> Plato, following his teacher, Socrates (and, it is likely, the older tradition of Pythagoras), understands philosophy as
philo-sophia, or, literally, a friend of Wisdom. This understanding of
philosophia permeates Plato's dialogues, especially the
Republic. In that work, the leaders of the proposed utopia are to be philosopher kings: rulers who are friends of
sophia or Wisdom. (
Wiki)
Again, we tread on shaky ground when we anthropomorphise spirits but here's an example of one given feminine characteristics, the scale of which were inconvenient to the male-oriented Church, hence the invention of "St. Sophia" much like the invention of "St. Valentine" to pave over existing fertility rites. What we really mean by Sophia is that font of wisdom in the human heart -- when it's allowed out to play.
More:
>> Who is Sophia? Literally she is Wisdom, because the Greek word Sophia means "wisdom" in English. More than that, Sophia is the Wisdom of Deity. She has been revered as the Wise Bride of Solomon by Jews, as the Queen of Wisdom and War (Athena) by Greeks, and as the Holy Spirit of Wisdom by Christians. She is known as Chokmah (pronounced HOK-mah with the H being said like -ch in the name Bach) in Hebrew, and Sapientia in Latin. << (
from here)
(Sapentia ... homo
sapiens)
We're off topic, except insofar as a religious massive sex change PR operation, part of which includes paving over the cult of Sophia and making her into a subordinate.