While Anneliese (with German, Hebrew, Dutch or Nordic origins) is lovely, one might also consider its Latin counterpart, Analicia (also Analisa and Analiza). http://www.behindthename.com/name/anneliese/comments
Anneliese Michel complained of seeing disturbing visions while saying her prayers. Was Anneliese Michel a victim of demonic possession or mental illness? http://www.historicmysteries.com/anneliese-michel-exorcism/