I know a family with 4 children who used E, A, I and O for the initials. I think E, A and I were coincidental but they thought it was funny and made a deliberate decision with O.
There are so many beautiful A names for girls. Lots of I too though I can't think of many U names I like.
Leaving aside very common names:
Arwen, Amaya, Astrid, Alba, Ariel, Amy, Aubrey, Amberley, Aria, Aliya, Abigail, Araminta, Aphra, Anika, Anoushka, Alannah, Avery, Ailsa
Imogen, Inez, Iris, Ingrid, Isadora, Iona