How about I ask my company to reassign a regular customer that I deal with?
Why do you want her reassigned?
She talks too much, I can't handle her anymore.
If you feel like you can't handle a customer anymore, then it would be appropriate to ask your company to assign her to someone else. Just make sure you are asking in a respectful way, and if they decline, then continue to deal with her professionally.
She drives me nuts. I want to hurt her and she won't leave.
That's okay for you to have someone else take on a customer that you don't agree with. Just ask them if they're willing to give her to another agent, and I'm sure that they would be happy to help.