I think that many fewer stars than you might expect actually have names. (I expect all the visible ones and more have some sort of code name these days, but there are seemingly no more than several hundred 'Polaris'es and 'Betelgeuse's.)
I think you've got a higher opinion of the patience of the ancients than I have. I was surprised there were as
many as a few hundred with individual names.
Most of the visible stars have deterministically-allocated code-names by the
Bayer or
Flamsteed schemes, both based on the constellation they're in and an order-of-brightness ranking within each constellation.
Peter
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