As a Greek who lives in Greece: we generally don't translate our names in english and I haven't seen that being done with english names either.
So, if your name is, for example, Sydney, theν you will write Σίντνεϊ.
Although, for a lot of names we have a certain spelling form, like Ντέιβιντ (David), Κόρεϊ (Corey) etc. So, you don't just match sounds to letters, a lot of times they are certain. Also, it's better to take the current form because a lot of english names don't have a translation to begin with.