They tend to refer to it as the "two lands" transliterated t3wj, pronounced something like 'ta-oo-ee' or 'ta-wee'.

It's based on Egyptian ideas of duality, both in political systems and cosmology.

The Egyptians saw a distinction between the 'red land' of the desert and the 'black land', the fertile floodplains along the Nile. They called this black land 'kmt', 'kem-et. They also saw a distinction between the east bank of the Nile, which represents life, and the west, death. This is why pyramids and tombs are on the west bank. Egypt was also originally separated politically and culturally into upper and lower, corresponding with the southern and northern parts of the country respectively. In the late 4th millennium, Egypt's first king, Narmer, united the halves, but some cultural and political distinctness was maintained.

So the 'two lands' is how Egyptians saw themselves, based on various notions of duality in their belief systems.

Sources: Allen, Middle Egyptian.

Kemet, or as written in Egyptian hieroglyphics, km.t, was the native name for Egypt. Kemet, an Egyptian word generally meaning 'black', is supposed to represent the fertile black Nile soil, as opposed to the infertile red soil of Deshret, which was the desert surrounding the Nile.

What was their name for their language?