Claudiu, if you just want a straight transliteration, you can take off the sigmas. But it's very unusual for a Greek name to end in just an upsilon, so I added the sigma to make it standard. Also, usually only female names end in an alpha, so I added a sigma to your last name to make it gender-neutral.
Richard, Rich's transliteration is correct, but if you want to make it more Greeky, you can do it Ριχάρδης (or Ριχάρδος) Ταλλάχος.
For example, I go by Χαρλῆς ̓Ιωάννου, which translates to "Charles, [son] of John."