Sounds incredibly dated, will go straight to Beverly Hillbillies, and any name with "beaver" as the primary meaning can't be good. All in all, a zero out of ten from me.
If you *must* use it, definitely throw it into the middle name spot and expect some complaints from the child. Alexis Beverly isn't great. I prefer Alexa or Alexandra Beverly. The flow seems to work better. Sorry to be so harsh on it, but it's just grating to me! :-P