You’re obviously too young to have heard of the British actresses Hermione Baddeley and Hermione Gingold! The older generation will, or at least should, remember those famous actresses.
The name Hermione predates Harry Potter the same as Wendy predates Peter Pan.
The association with Hermione Granger is a positive association and I think it’s silly for you to not name your daughter a name you like because of a positive literature association.
Hermione was not unheard of in the UK before Harry Potter. In fact, if you read the other threads about this name you will read that people know one, two or even a few people with the name.
Also, you may be surprised to know that Hermione was a common name in Asia Minor, from Names of the Week - British Baby Names:
“There are several examples of Hermione in use in the Classical and Hellenistic Greek eras. The Lexicon of Greek Personal Names has recorded 107 examples of the name in use, many of them in Asia Minor where it was around the 11th most popular name for women.
Hermione was also not uncommon in the Roman Empire, often found in the Latinised form Hermiona. St Hermione (d.117) was a Christian martyr of Ephesus, while Pompeii sports the tomb of a Lollia Hermiona.”
I have a friend with the name who told me a few years ago that Harry Potter has helped more people pronounce the name correctly. I don’t know anyone else with the name personally, but I used to work with a girl with the name, although I never spoke to her.
It’s not a popular name, but it is a relatively common name and pops up every now and then. In fact, the new programme Love in the Countryside on BBC Two featured a woman called Hermione on the first episode.