Since I'm a naturalized US Citizen, I'm not sure if I (the petitioner) should leave this blank or complete?

You should complete this portion of the form if it is applicable. For more information, please see

If you are a US citizen and the petitioner, I wouldn't worry about it and leave it blank on your G-325. Otherwise, "Native" means exactly that. Since you were taught a different alphabet than Latin at birth, you could type in your name in your Native Alphabet if you wanted to, but at this point, being a USC I don't see why you would..

If you were originally taught a different alphabet, before you learned English and learned the Roman allhabet, then this would still be considered your native alphabet and you should write your name in your native alphabet in the space provided on the form.