Annabel. Either MN. Addison is just too trendy for me, even with significance.
Adeline, Annabeth, Angeline, Annemarie, Annalise, Aurelia (3 syllables depending on pronunciation), Althea, Abigail, Amelia, Audrina, Adria, Adelaide, Angelique, Alicia, Augusta, Adela, Ariane, Allison, Alaina