Amabel is an older name than Annabel and a lot more distinctive. Amabel was a very common name in the twelfth and thirteen centuries, then was revived during the nineteenth century British fad for medieval names.
In a short story by H.H. Munro, about Amabel, the vicar's daughter, it is said "Her name was the vicar's one extravagance."
Amabel's shortened form Mabel overtook the mama name early on.