I've seen plenty of elderly women with the full name
Annie and it seems to have served them quite well. I have the same opinion of long held nicknames as first names like
Molly,
Penny and
Sally.
I like
Anne,
Anna,
Annabel but I like
Annie equally well. If anything, I find it more unexpected in this day and age. I know in some places nicknames
Katie,
Evie etc have taken off but I still never see
Annie used.