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
"Anissa
Mariam Bouzianne, an Arab-American writer and filmmaker" (
http://www.religioustolerance.org/dixon_011.htm)
"Anissa
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).
"
Mary 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." (
http://www.franksreelreviews.com/shorttakes/anissajones.htm?sourceid=00387356854394375831&ISBN=158754010X&bfdate=07-26-2002+08:07:40)
"
Mary Anissa Jones (...)Anissa is pronounced "Ah-NEES-ah" (rhyming with
Lisa not
Melissa) and in Arabic means "little friend"." (
http://psychcentral.com/psypsych/Anissa_Jones)
"
Mary 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.
Lumia
http://onomastica.mailcatala.com