Although the equation “my identity = my language = my ethnic group” does not always hold water (a good example are the Hazaras of Afghanistan, a people descending from Mongol tribes who are Persianised to the extent that Persian has become their mothertongue) it can be argued that in the case of the Persian speakers in Iran it does.
Whatever the case, there is no doubt that the majority (around 60%) of Iranians are known as Fars (although most Fars/Persians often simply refer to themselves as Iranians). A Fars (a Persian) in Iran is someone whose mother tongue is Persian (Farsi, sometimes along with a sublanguage) or traces himself back to ancient Persians.
Having said that, there are regions of Iran where one still can find pockets of Persian Sunni communities, especially in the Khorasan (north and south, even in Mashad!) province of Iran and in the far south of Iran like Hormozgan and the south of the Fars (Persia!) province where the ancient Persians were present from about the 10th century BC, and became the rulers of the largest empire the world had yet seen under the Achaemenid dynasty. The people inhabiting that region (south Iran) today are a majority Sunni people who trace themselves back to the ancient Persians and often proudly state that they are ethnically and linguistically more Persian than northern Persians.
The predominantly Sunni people in south Iran are known as Achomi (also as Lari or Larestani people or Khodmooni). They are a Persian ethnic group who inhabit primarily in Southern Fars, and Hormozgan Province, Iran. Significant numbers of Achomi people have migrated to Kuwait, Bahrain, UAE and other Persian Gulf Arab countries in the region.The historical region of Irahistan consists of several counties in Fars Province (Larestan, Khonj, Gerash, Lamerd) and Bastak County in Hormozgan. In Bahrain, Sunni Bahrainis of Achomi ancestry are a well respected community and often speak the Achomi (which is considered a language closer to ancient Persian than modern day Farsi) language .
On our new banner on the rightside bar will link you to posts about Persian Sunnis of Iran, at the very least this is how these communities (Lari/Achomi Shafi’i Sunnis and Khorasani Hanafi Sunnis) mostly identify themselves (unlike other ethnic groups in Iran such as the Baloch Sunni, Kurdish Sunnis etc.).