Am a fan of Carys (my DD is Cerys - same meaning just the other spelling - there are not many of either spelling about so is quite unique but still has traditional link as is Welsh), and I think does go well with Alexander - I know one is short and one is long but I think Carys and Alexander do go well together. Alexander is quite a traditional name was a royal name in Scotland so I think having two Celtic names is also good.

Although Georgeanna and Alexander both have Greek origins so there is the link there too. To me though probably because grew up in UK, when I think Alexander I think Scotland so that is why I personally would pick Carys to go with it.