Egypt was called Khemet in the early period (Old Kingdom) and later Misr (a name that remains even today) but I am wondering when they changed the name from Khemet to Misr, what century would be considered a good precision answer, if possible.
The ancient Egyptians thought of their country as two parts: kmt or "Khemet" (meaning "The Black Land" - a reference to the fertile strip along the Nile), and dšrt or "Deshret" (meaning "The Red Land" - referring to the deserts beyond that fertile strip). As you say, they referred to themselves as Kmtyw or "The people of the Black Land" from at least the Old Kingdom (and possibly earlier).
[kmt / dšrt / Kmtyw are transliterations from the hieroglyphs. As with some other languages in antiquity, the written forms of the ancient Egyptian language did not include vowels, so transliterations are often written with added letters (often the letter "e") to aid pronunciation]
Even as late as the Persian occupation of Egypt from 525BC to 332BC, the name kmt or "Khemet" is used for the name of Egypt on statuary and hieroglyphic inscriptions.
Throughout the Graeco-Roman period kmt was still used as the name for Egypt in hieroglyphic inscriptions (it appears 3 times on the Rosetta Stone, dated to 198BC), while the Greek name, Aegyptos, tended to appear in Greek and Latin texts.
Misr is the Arabic name for Egypt, and so it's use by Egyptians as the name for Egypt probably dates to the Arab conquest of Egypt in the mid 7th century (~640AD). There are several theories for the origin of Misr as the Arabic name for Egypt.
I copied your question into google; the second result gave me the answer.
Then from 525 BCE non-African rulers controlled Kemet, which became known as Egypt under the Macedonians and Ptolemaic rulers. Then in 642 CE Egypt became the Arabic Misr. Kemetexpert