As you know there is no translation of the name. I can offer a transliteration using the Greek alphabet. The name Carrie in Greek would be :
Κάρρι - first letter in capitals
κάρρι - all lowercase
ΚΑΡΡΙ - all capitalized

This particular name tends to not even be transliterated in most Greek sites. Only a few have it in Greek letters. I cite one of them placing the name in between asterisks

... Πρωταγωνιστές : Κιάνου Ρηβς, ***Κάρρι***-Ανν Μος, Λώρενς Φίσμπερν, Μόνικα Μπελούτσι, Ντάνιελ ... http://tinyurl.com/yva9g

--------------------------------------------------
Note added at 8 mins (2004-05-20 01:59:28 GMT)
--------------------------------------------------

Also other sites have your name transliterated in the Greek language but simplifying it by \"eliminating\" the second r .. That would look like this :

Κάρι - first letter in capitals
κάρι - all lowercase
ΚΑΡΙ - all capitalized

... Καστ: Κιάνου Ριβς, Λόρενς Φίσμπερν, Κάρι-Ανν Μος, Χιούγκο Γουίβινγκ κ.α. ... homepages.pathfinder.gr/cfreak/20030201_archive

Κιάνου Ριβς, Λόρενς Φίσμπερν, Κάρι-Ανν Μος,. ... homepages.pathfinder.gr/cfreak/movies

... βασικούς πρωταγωνιστές, τον Κιανού Ριβς, τον Λόρενς Φίσμπερν, την Κάρι Ανν Μος και τον ... www.videorama.gr/details.asp?ProductId=42468

Νο sopecific fascination with Carrie Ann Moss .. I just found it easier to look up the name using hers as a search base.

--------------------------------------------------
Note added at 9 mins (2004-05-20 01:59:59 GMT)
--------------------------------------------------

Correction : sopecific = specific