As much as Afrocentric groups teach this, it actually doesn't translate that way. "Khem" or "Kem" translates directly as "black". The "et" in "Khemet"/"Khemet" is what translates as "land".
There's no reference to the face. If I'm remembering right "face" is "mesu" or "mesa", something with an m. If one were to say "Land of the Black Faces" it would come out as "Khemet em Mesu" or "Kemet em Mesu" (assuming mesu is correct).
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I'm not white-washing when I say that ancient Egypt didn't consider race an issue; they really, really didn't. It didn't matter what level of pigmentation existed in your skin; what mattered was the nationalism in your heart. If you were of Khemet/Kemet, you were of Khemet/Kemet. They only got particularly vicious towards foreigners/foreign lands which refused to submit to their authority. This is why the Nubians/Kushites had such issues intergrating into ancient Egyptian society until they were, literally, the most authentic ancient Egyptians.
(Originally they were considered lesser, because they were a colony society. When ancient Egypt fell and the Nubian/Kushite empire rose to glory, eventually overtaking Egypt from the foreigners, they were hailed as bringers of Ma'at and destroyers of opression. This is because they, although a colony, had kept the traditions of the ancient Egyptians more fully than their Egyptian brothers; the ancient Egyptians had forgotten themselves in the oppression they found themselves under.)
Although the Nubian/Kushite dynasty didn't last long, it was important. Even more so because modern day white-washing refuses to recognize their existence as a dynasty; there is a Muesum (I believe the one in Cario) which exhibits plaques around the building stating the dynasties and how long they lasted, the 24th Dynasty - the Nubian/Kushite dynasty - is the only one missing. When the building was put in place, they were not considered an authentic ancient Egyptian dynasty. To my knowledge this error has never been corrected.
White-washing happens and I highly respect those within the Afrocentric movements which attempt to address these issues, what you are stating is simply untrue. If we have to go into ethnic origins, ancient Egyptians would look like modern day Egyptians and other inhabitants of the Middle East. I wouldn't necessarily call anyone of Middle Eastern origin "black", simply because I a) am not black, b) am not Middle Eastern, and c) haven't spent time researching the proper term for it.
TLDR: The ancient Egyptians would definitely have been "People of Color" and definitely would not have been white. ("People of Color" is used due to a reclaiming of the phrase by non-white persons. I simply use the term I have been told is appropriate to use.) However people of fairer skin would have been accepted into society, were they to adopt the culture and attitudes of ancient Egypt.