Anissa is the "correct" transcription in French and Catalan because the double SS represents a [s] sound and the simple S represents a [z] sound. In Spanish, the tanscription Anissa is not correct because there is not SS, but sometimes this group is used because of French/English influence.
In English, the more usual (and correct according my Arabic names book) transcription is Anisah, but I found it spelled Anissa, too:http://www.proz.com/kudoz/9333?float=1
Bouzianne, an Arab-American writer and filmmaker" (http://www.religioustolerance.org/dixon_011.htm
Language of origin: Arabic
Variants: Anissa Arabic (#680 in US popularity) " (http://www.aboutnames.ch/HWA.htm
Probably the name was popularised in US by Anissa Jones, but her name was Arabic (and very used in Lebanon).
Anissa Jones was born in West Lafayette, Indiana
to Purdue students John
P. Jones and Mary
P. Tweel on March 11, 1958. Pronounced , her name is Lebanese and means "Little Friend
Anissa Jones (...)Anissa is pronounced "Ah-NEES-ah" (rhyming with Lisa
) and in Arabic means "little friend"." (http://psychcentral.com/psypsych/Anissa_Jones
Anissa Jones (...) Her name, Anissa, was Lebanese for 'little friend'." (http://www.imdb.com/name/nm0427490/bio
I don't know, obviously, if her parents have a Lebanese/Arabic background, if they knew the name from a book or from a friend, for example, etc., but the origin of her name is Arabic.