Sibyl is the more authentic spelling. My guess is that the
Sybil spelling came about because of confusion with
Sylvia. I have no data on that. It took me a little getting used to because I used to spell it
Sybil too. But it's not that difficult and I'm glad I did.
The authenticity is the most important to me. But I also like
Sibyl visually. The "y" at the end looks more at home. This is an odd turn of my mind, but the "y" looks heavier than the "i" and so seems to belong after it.
I was so enchanted with the notion that you loved the name that I dind't even notice when I left my comments above.