They were called Huaxia at the time of their ethnogenesis (as well as other names at different points in history) AFAIK, but they're still the same people in question.
So which region of China did Hans originate?
The earliest that "ethnic Chinese" can be placed with certainty is the 13th century BC, when the Shang were writing divination records in what was clearly an ancestral form of the Chinese language. Shang materials have been found over a large part of north China but concentrated around Yinxu in Henan, identified as their last royal capital. We can confidently identify the late Shang as "ethnic Chinese" because their language shows continuity with later forms of Chinese; their material culture shows continuity with Zhou and later cultures; and Zhou and later texts explicitly refer to them as Huaxia.
Earlier cultures in north China, like the Erligang (15th century BC) and Erlitou (19th-15th centuries BC) are ancestral to the Yinxu culture in the material sense, but they lacked writing and therefore we can't be certain whether they spoke Chinese, another language, or a mix of languages (in the better-documented Zhou period, for example, we know that South China and the northern steppe were each home to numerous distinct language families- the same could have been true of early North China). So while many Chinese archaeologists and historians identify these material cultures with the Xia and early Shang and therefore as ethnic Chinese, this is not widely accepted outside of China due to the lack of written evidence produced by the cultures themselves.
In short, we can be very confident that there was a Huaxia ethnicity at least by the 13th century BC, and at least around the middle reaches of the Yellow River, but because of the nature and availability of evidence the further back you go in time, or the further you get from Yinxu, the less certain things become.