结论：埃及人从古至今都不是自称“埃及”，埃及是从希腊人开始的讹称。古埃及自称 km.t（我们可以音译为“库马特”），阿拉伯人征服之后称为 Misr，埃及方言称为 Masr，中国古代有译名为"密思儿"，就是这么来的。

从维基百科的 Egypt 词条中其实就可以查到这个信息。

首先是古埃及的自称：

The ancient Egyptian name of the country was km.t, which means black land, likely referring to the fertile black soils of the Nile flood plains, distinct from the deshret(⟨dšṛt⟩), or "red land" of the desert.[22][23] This name is commonly vocalised as Kemet, but was probably pronounced [kuːmat] in ancient Egyptian.

简单翻译一下，就是说 km.t.在古埃及语里意思是黑土地，即是因尼罗河泛滥而变得肥沃的土地，与沙漠地带“红土地”所区别。

从科普特语（古埃及语的直系后裔）对埃及土地的自称 Kimi 也可以看出 km.t 这个名字的影子。

Miṣr (IPA: [mi̠sˤr] or Egyptian Arabic pronunciation: [mesˤɾ]; Arabic: ‎‎) is the Classical Quranic Arabic and modern official name of Egypt, while Maṣr or Masar (IPA: [mɑsˤɾ]; Egyptian Arabic: ‎‎) is the local pronunciation in Egyptian Arabic.[18] The name is of Semitic origin, directly cognate with other Semitic words for Egypt such as the Hebrew מִצְרַיִם‎ (Mitzráyim). The oldest attestation of this name for Egypt is the Akkadian KURmi-iṣ-ru miṣru,[19][20] related to miṣru/miṣirru/miṣaru, meaning "border" or "frontier".[21]

这一段讲的是现代埃及的自称“密思儿”的由来，题主问题不在此就不翻译了。

The English name Egypt is derived from the Ancient Greek Aígyptos (Αἴγυπτος), via Middle French Egypte and Latin Aegyptus. It is reflected in early Greek Linear B tablets as a-ku-pi-ti-yo. The adjective aigýpti-, aigýptios was borrowed into Coptic as gyptios, and from there into Arabic as qubṭī, back formed into qubṭ, whence English Copt. The Greek forms were borrowed from Late Egyptian (Amarna) Hikuptah "Memphis", a corruption of the earlier Egyptian name (⟨ḥwt-kȝ-ptḥ⟩), meaning "home of the ka (soul) of Ptah", the name of a temple to the god Ptah at Memphis.[17] Strabo attributed the word to a folk etymology in which Aígyptos (Αἴγυπτος) evolved as a compound from Aigaiou huptiōs(Aἰγαίου ὑπτίως), meaning "below the Aegean".

最后是“埃及”这个名字的由来。实际上就是希腊人把埃及的一座神庙的名字 Aígyptos 当成了埃及的国家名称，这个事情就相当于有人用“长城”、“天安门”或者“天坛”来当成中国的名字一样（想象一下你被称为“长城人”是多怪异）。之后又辗转多门语言流传开来。最重要的一条路线是进入拉丁语 Aegyptus，然后法语，最后到英语便是 Egypt。大多数不在中东的国家对埃及没有直接了解，获得的信息都是从西班牙人、英国人等殖民者那儿获得的，因此便跟着他们把尼罗河下游的那个国家称为“埃及”。

其实题主所提的 chinese（来自于 China）也正是一种讹变而来的称呼，并不是那个民族自己的真正名字。这个是题外话了。