possibly they will be advised not to use anything seen as too pretentious ,remember the slating fergie had for eugenie. that probably rules ot augusta and alberta (although cannot imagine many 30 year olds who find that appealing). caroline again would probably be too of their own generation iyswim ( i know quite a view in their 30's and early 40's)
patrick as a first name possibly perceived as to irish and they wouldn't want to upset the scots and the welsh . same probably applies to david , andrew and duncan someone in the union would be miffed.
i don't envy her it was hard enough finding names without worrying about upsetting half the country.
Unity might hit the right note or even Prudence
Mary could in some circles could be seen as too papist daft but true
i think her grandmother was Dorothy or Dorathea so Theodora might be in with a chance
the childs surname will be mountbatten not windsor .as i think when the Queen married Philip there was some agreement that his surname or it's anglicised form would be used for the great grandchildren
Margaret might be an option
Arabella also might be an option lady arabella stuart was once a contender for the throne arabella stuart
or if she's having a really hormonal moment she could always try Tiaamii 