How to write the name kathryn in greek?

There isn't a direct, single perfect translation of "Kathryn" into Greek. The name's origin is Greek (Katharine, derived from "katharos" meaning pure), but modern usage varies. Therefore, you could use several options depending on the nuance you want to convey:

* Καθαρίνα (Katharina): This is a very common and direct transliteration of Katherine/Kathryn. It's probably the closest and most easily understood option.

* Αικατερίνη (Aikaterini): This is another very common Greek form of the name Catherine, and it's also widely accepted. It's perhaps a slightly more traditional or formal sounding option.

* Καθηρίνη (Katherini): This is a less common but still perfectly acceptable variation.

The best choice depends on personal preference and context. Καθαρίνα (Katharina) or Αικατερίνη (Aikaterini) are your safest bets for clarity and widespread understanding.