Does Gwyneth Alice sound like a nice name?

I want to use the name as the protagonist in a story I'm writing, mostly because the name is ironic (she is NOT happy and is NOT "noble or exalted" in any way), but also because I think it sounds nice. I told my mom about it last night, and she said it didn't really flow together. Does it flow well together? If not, what other middle name could I use? I definitely want to use the name Gwyneth, but I suppose the middle name is subject to change. Thanks.