Annika is my favorite, too.
I'd use a variation as well. My favourites are:
Love the nn Nina.
Isn't Nina the Russian form of Anne? Nina is short for Antonina, and that starts with An...
I ADORE Anaïs. I think it is so beautiful but also poses some promunciation problems here in the U.S. although the rest of these, while all lovely names, I have to say, aren't quite my style.
I'd use some variation of the names too.
Annabel, Annika are great choises.
Orpossibly a double-barrelled combo like Anna-louise, Anna-Sophia. Or something like Marianne, Luciana or the like. But my suggestions dont get you to Nina, sorry.