While Anneliese (with German, Hebrew, Dutch or Nordic origins) is lovely, one might also consider its Latin counterpart, Analicia (also Analisa and Analiza). I have found that it means "graced with God's bounty" regardless of the root language. I must admit, however, that I'm biased to the Latin versions because my name is Analicia Marie. I've met girls with variant spellings but never exactly like mine. I prefer to pronounce it Ah-nuh-lee-see-ah like you would in Spanish. However, most people I meet (English-speaking Americans) pronounce it Ann-uh-lee-shuh. When I was a kid it bothered me that it was different and "difficult" but now I absolutely adore it.
I've traced this name back to the name Channah and Elizabeth. The name Hannah is derived from Channah and Anna is derived from Hannah. Liese is a pet form of Elizabeth.