Apparently a Hebrew or even Arabic word.

1. Old Semitic word for the letter "O"
Subject: The Semitic Roots of Latin Alphabets

O = Ayain. Illiteracy of Southern Semitics made them use it more than 'O'.
* Aayin was picture of a sitting straight owl looking at you so it became an Oval and a small circle first. Then right-hand side of the owl started missing and this is how present Arabic Ayain looks like. In Latin, the small circle is missing but when you write it in running hand, you are still trying to make the that little circle still.

2.In Chaucer's English it must have meant "against"
This knight," he seyd, "that stont me bi,
Wil fight for th'erl sir Tirri
(For no thing wil he wond),
And defende him of that felonie
Ayain the douk Berard of Pavi
That he berth him an hond;
For Tirri is out of lond went
To seche Guy, verrament,
That for him might stond


3.Nowadays, it can be an Arabic name for sure:
e.g.
Welcome to Aya-chan's Angels! We are Orfos and Ayain the Webmistresspie of the site! This site started out as Mastermind x2 a Shrine to Schuldich but Orfie decided she loves all the assassins and realized she was about to make shrines to all the assassins from Weiك Kreuz. Now it is Aya-chan's Angels a Weiك Kreuz Shrine and Info Site made by both Ayain and Orfie!

http://www.tidalweb.com/weiss/main.html



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Note added at 1 hr 15 mins (2003-08-20 20:24:56 GMT)
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Merriam-Webster Dictionary definition:
Main Entry: ayin
Pronunciation: \'I-&n
Function: noun
Etymology: Hebrew \'ayin, literally, eye
Date: 1823
: the 16th letter of the Hebrew alphabet -- see ALPHABET table

http://www.webster.com/cgi-bin/dictionary?va=ayin