Yeah, Hermione's middle name is Jean, and I agree that that could possibly be her mother's name. On the HP-Lexcon, it says that we do not know her parent's names. So, I think you could have free rein with that.
However, if you need any help with coming up with names, I always called Hermione's dad "John". I don't know why, but he always seemed like a 'John' to me. Her mother, I never really thought about, but could pass as a 'Jean'. Originally, Hermione's middle name was 'Jane', until JKR changed it in Book seven. I like "Jane' better. Maybe her mom's name could be Jane, but they switched the letters around for a middle name for Hermione. Just a thought.
Also, for anything else you may need to know about Hermione, she has an entire page on the HP-Lexicon. You can find her
here.
I hope you don't regard what I said as a mess of words, and if you have any more questions, please feel free to PM me!
~Andrea