I really like Annika, and find that a good reiteration of "No my name is Annika, its not Ann/a/i works.

I voted for Fay for the middle name more for how the two names flow - I prefer the other middle names but i think one syllable sounds better.

I love Elke and Savannah

Hmm other suggestions

Silke
Anja
Dimity
Liana
Zari
Adelita
Danica
Lori
Lorelei
Olanda
Verity