I'm a little bit envious. Reading such a great book for the first time.
I recommend re-reading it in a few years. Ecos books grow with you; the more you learn about the world and history, the more you'll find in nuance in that book. Maybe more true for me - as a teenager I've read it first as a mostly weird detective story. Later re-reads made me more interested in the weird parts.
There is, by the way, a separately published Postscript to the Name of the Rose with some notes on writing the book.
Nice pull.