I actually think of a Winters Tale first, I know its not the best play ever but I really like the name, I also think of
Helen of
Troy's daughter, who was named
Hermione.
There are several actresses and such named
Hermione, so it does have some other known useage:
http://www.imdb.com/find?s=all&q=hermione
But I agree, lots of people, for the mean time, will associate it with
Harry Potter. But as time goes on, the books will fade out of peoples memory. At least now people know how to pronounce the name!