English. Possibly from Latin "lovable" [see Amanda] but ONC suggests it is a dissimilated form of Amabel.
Used in Scotland for at least eight centuries, it is occasionally an Anglicized form of the Scottish Gaelic Barabal [= Barbara].
A correspondent [MT] has pointed out that, in the county of Argyll, Scotland, Annabel/Annabella may be used interchangeably with Neps. We have not been able to find any authority on this and consider the latter is probably a pet name. However there are six records of a baptism for Neps, all in Argyll, so it is at least a valid given name and may be a synonym for Annabel/Annabella.