Sarah to her credit gave her daughters very old royal names. I don't know if Eugenie is a family royal name or one from another royal family but it shows that Sarah has knowledge of history. Maybe Eugenie will do the same. I looked up Andrew's names I must say that Christian surprised me although I like it. I like Albert a lot too. I love the name Alice also Amelia and Louise. Philip would be a wonderful name for a boy.
Maybe Sarah was thinking of Empress Eugenie of France?
What about the story of Sarah wanting to name Beatrice Annabelle and the Queen stepping in and forbidding it?
Probably more likely The Queen Mother rejected it...lord knows she never gave up control. I can't see they same person rejecting Annabelle but approving **Savannah, Isla, Mia, Lena, or Archie**...unless she only care about the HRHs, which is possible. But, as always, I could be wrong.
**None are very "royal" but then again Zara isn't a very royal name either...that may be do to the HRH approval only theory.
I remember reading that Charles suggested the name Zara to Anne, who apparently liked it enough to use it. As for Annabel, which is the spelling I believe Sarah wanted, it's way too close to Anne, and since both would be Princesses I can see why Sarah would have been told to choose again.
Whether or not HM gets to 'approve the names', I believe she only really cares about the names of those who are in the direct line of succession anyway.