Genesis 10:13

And Mizraim begat the Nivatee, and the Mariotee, and the Livakee, and the Pantascinee,

AND MITZRAIM BEGOT. Scripture mentions the descendants of Mitzraim but does not specify their habitation as it does concerning the others. With the sons of Japheth it mentioned the isles, with the sons of Cush it mentioned the land of Shinar and Asshur, and with the sons of Canaan it mentioned the boundaries of their land, and likewise with the sons of Shem. This was because Mitzraim (Egypt), the land of his habitation, was known for it was called by his name, and all his children lived around Egypt, and the names of their countries were also like their names. Thus we find for Pathrusim, [one of the children of Mitzraim], the land of Pathrus, which is part of the land of Egypt, as it says, And I will put a fear in the land of Egypt. And I will make Pathros desolate; Into the land of their origin., 29:14. The verse reads: And I turn the captivity of Egypt, and will cause them to return into the land of Pathros, into the land of their origin. This shows that the land of Pathros is near Egypt. Similarly, Lud and all the Arabians, 30:5. were also around Egypt, and the names of their countries were like their names. So also the land of the Philistines was called Philistia, and so it is written [in Exodus 15:14], the inhabitants of Philistia.
But Rabbi Abraham ibn Ezra said that these [names — Ludim, and Anamim, etc., in Verses 13-14] — are names of countries, and in each and every country there dwelled one family. This is why the names are all in the plural form, [that is, on account of the persons in the family, hence Ludim and not “Lud”]. And the real proof [that these are names of countries is the expression], ‘misham’ (whence) went forth, for this word misham alludes to a place. In the opinion of the commentators, the meaning of the expression, that went forth, is that they begot them, just as in the expression, And kings shall come out of thy loins. Now Rashi wrote: “They [the Philistines] were descended from both of them [the Pathrusim and the Casluhim], for the Pathrusim and Casluhim used to live together in promiscuous intercourse, and the Philistines were their offspring. Thus in Bereshith Rabbah.”
In my opinion, by way of the plain meaning of Scripture, the Casluhim dwelled in a city of that name — which was part of the land of Caphtor where the Caphtorim their brethren were — and they went forth from there, meaning from the Caphtorim who were of the seed of Casluhim. And they went in order to look for a resting-place for themselves, and they left the land to their brethren and conquered for themselves a land by the name of Philistia, after which they came to be called Philistines. This is why Scripture says, The Caphtorim, that came forth out of Caphtor, destroyed them, and dwelt in their stead, the Caphtorim being of the sons of Casluhim, dwellers of the land of Caphtor.

ומצרים, we do not know why Cham called the name of his son מצרים with the letter י, and the letter ם at the end. We do not find a parallel to this except amongst the sons of יון in verse 4, who was a descendant of Yaphet, where we encounter כתים and דודנים. (plural mode) Perhaps, the spelling of the name מצרים is related to something that happened at the time he was born. Most names in those days were related to some incident of which the father had foreknowledge and wanted to be remembered. According to Bereshit Rabbah 37 all the offspring of מצרים listed are spelled with the ending ים. This ending, which also means yam, sea, is an allusion to the Egyptians being drowned in the sea.