I have heard of the male surname Óõñßãïò(Syrigos), but never of the female name Óõñßãù (Syrigo). Many female names ending with an omega are informal (and somewhat "bucolic" for lack of a more appropriate term) and imply "wife of so and so".
My speculation is that you heard the name in some Greek village, and the Syrigo in question is the wife of a fellow with the surname Syrigos. Elementary Watson? Maybe not!
Now, what could the meaning of Syrigo / Syrigos be? Here are two quasi-educated guesses:
- From Syros, an Cycladic island, or from Syria
- The name could ne related to the verb óõñßæù (syrizo) meaning "to whistle".