From the experts:
Susanna is an old and under-appreciated name, perhaps because of the recent overpopularity of Susan, that is certainly due for a comeback.
The Susannah spelling is just as appropriate as Susanna. The two versions seem to have traded places over time as the dominant version. Neither spelling is in the Top 1000 at the moment, though we expect that will change over the next few years as more modern parents rediscover these beautiful Biblical names.
How is Susanna different from Susannah? The h-less version feels a bit more streamlined and modern, and might refer more directly to an ancestor named Ann or Anna. Susannah seems more old-school Biblical and more self-contained, while Susanna resembles a smoosh name: Sue + Anna. But Susanna and Susannah are pronounced the same and are equally beautiful.
A European short form of Susanna that's become popular: Sanna or Sanne.