You could say that in the U.S. everyone would know who the vice president is. First female vice president. It's historic.
Sure, you could say that everyone would know.
Now go do some street interviews. You'll find out quicker than you like what people actually know versus what you think they should know. And this is in a country with free public education for everyone.
Transition over to a society filled mostly with uneducated peasants, all split apart by assorted boundaries. In a land filled with numerous races and monsters and bandits and wizards and this symbol and that symbol. No, the average person doesn't know a tenth of what the typical Forgotten Realms fan does, especially considering the fan has probably spent years reading setting books.
It's a common mistake, the inability to see the trees for the forest.
A farmer would see that circlet and armor and think: rich. Not Shar.
Someone who made a study of religion and symbols *might* put one and one together, assuming they made an appropriate DC check. But even then, I would expect them to know she was a cleric first.