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According to this site, the name 'Ansam' is a Danish corruption of the German name, 'Anselm'. It means 'divine guardian'.
http://rjg42.tripod.com/NEWBOYA.htm -scroll down to the entry, 'Anselm'
I saw the Arabic horse site- I believe you were directed there for the translation, which said that Ansam meant, "breath of life".
Now I did find AnXXXXX XXXXXsted on a site of baby girl names, here: http://babynames.indastro.com/arabicthreefA.html- However, the link on that page to find the meanings of these names does not work.
Lastly, this is a site of traditional arabic songs. There is a track titled, "Ansam" and in parentheses it says, 'breezes'. http://www.artistdirect.com/nad/store/artist/album/0,,82566,00.html
I am inclined to believe that breezes or breath is the best translation. I have gone to translation sites on the web, but the word is not listed (possibly because it is a name).