Two things especially are observable in this account of the posterity of Shem: -
I. The description of Shem, Gen 10:21. We have not only his name, Shem, which signifies a name, but two titles to distinguish him by: -
1. He was the father of all the children of Eber. Eber was his great grandson; but why should he be called the father of all his children, rather than of all Arphaxad's, or Salah's, etc.? Probably because Abraham and his seed, God's covenant-people, not only descended from Heber, but from him were called Hebrews; Gen 14:13, Abram the Hebrew. Paul looked upon it as his privilege that he was a Hebrew of the Hebrews, Phi 3:5. Eber himself, we may suppose, was a man eminent for religion in a time of general apostasy, and a great example of piety to his family; and, the holy tongue being commonly called from him the Hebrew, it is probable that he retained it in his family, in the confusion of Babel, as a special token of God's favour to him; and from him the professors of religion were called the children of Eber. Now, when the inspired penman would give Shem an honourable title, he calls him the father of the Hebrews. Though when Moses wrote this, they were a poor despised people, bond-slaves in Egypt, yet, being God's people, it was an honour to a man to be akin to them. As Ham, though he had many sons, is disowned by being called the father of Canaan, on whose seed the curse was entailed (Gen 9:22), so Shem, though he had many sons, is dignified with the title of the father of Eber, on whose seed the blessing was entailed. Note, a family of saints is more truly honourable than a family of nobles, Shem's holy seed than Ham's royal seed, Jacob's twelve patriarchs than Ishmael's twelve princes, Gen 17:20. Goodness is true greatness.
2. He was the brother of Japheth the elder, by which it appears that, though Shem is commonly put first, he was not Noah's first-born, but Japheth was older. But why should this also be put as part of Shem's title and description, that he was the brother of Japheth, since it had been, in effect, said often before? And was he not as much brother to Ham? Probably this was intended to signify the union of the Gentiles with the Jews in the church. The sacred historian had mentioned it as Shem's honour that he was the father of the Hebrews; but, lest Japheth's seed should therefore be looked upon as for ever shut out from the church, he here reminds us that he was the brother of Japheth, not in birth only, but in blessing; for Japheth was to dwell in the tents of Shem. Note, (1.) Those are brethren in the best manner that are so by grace, and that meet in the covenant of God and in the communion of saints. (2.) God, in dispensing his grace, does not go by seniority, but the younger sometimes gets the start of the elder in coming into the church; so the last shall be first and the first last.
II. The reason of the name of Peleg (Gen 10:25): Because in his days (that is, about the time of his birth, when his name was given him), was the earth divided among the children of men that were to inhabit it; either when Noah divided it by an orderly distribution of it, as Joshua divided the land of Canaan by lot, or when, upon their refusal to comply with that division, God, in justice, divided them by the confusion of tongues: whichsoever of these was the occasion, pious Heber saw cause to perpetuate the remembrance of it in the name of his son; and justly may our sons be called by the same name, for in our days, in another sense, is the earth, the church, most wretchedly divided.

Peleg - From פלג palag, to divide, because in his days, which is supposed to be about one hundred years after the flood, the earth was divided among the sons of Noah. Though some are of opinion that a physical division, and not a political one, is what is intended here, viz., a separation of continents and islands from the main land; the earthy parts having been united into one great continent previously to the days of Peleg. This opinion appears to me the most likely, for what is said, Gen 10:5, is spoken by way of anticipation.

And unto Eber were born two sons: the name of one was Peleg,.... Bochart (k) thinks, that either Peleg, or one of his posterity, in memory of him, gave the name of Phalga to a town situated on the Euphrates; though the reason of the name, as given by Arrianus, as he himself observes, was because it divided between the two Seleucias, as the reason of Peleg's name was:

for in his days was the earth divided; among the three sons of Noah, and their respective posterities; their language was divided, and that obliged them to divide and separate in bodies which understood one another; hence that age, in which was this event, was usually called by the Jews the age of division; whether this was done about the time of his birth, and so this name was given him to perpetuate the memory of it, or in some after part of his life, and so was given by a spirit of prophecy, is a question: Josephus, Jarchi, and the Jewish writers, generally go the latter way; if it was at the time of his birth, which is the sense of many, then this affair happened in the one hundred and first year after the flood, for in that year Peleg was born, as appears from Gen 11:11.

and his brother's name was Joktan, whom the Arabs call Cahtan, and claim him as their parent, at least, of their principal tribes; and say he was the first that reigned in Yaman, and put a diadem on his head (l); and there is a city in the territory of Mecca, about seven furlongs or a mile to the south of it, and one station from the Red sea, called Baisath Jektan, the seat of Jektan (m), which manifestly retains his name; and there are a people called Catanitae, placed by Ptolemy (n) in Arabia Felix.

(k) Phaleg. l. 2. c. 14. col. 93. (l) Vid. Pocock. Specimen. Arab. Hist. p. 39. 55. (m) Arab. Geograph. apud Bochart. Phaleg: l. 2. c. 15. col. 98. (n) Geograph, l. 6. c. 7.

Peleg; for in his days was the earth divided--After the flood (Gen 11:10-16) the descendants of Noah settled at pleasure and enjoyed the produce of the undivided soil. But according to divine instruction, made probably through Eber, who seems to have been distinguished for piety or a prophetic character, the earth was divided and his son's name, "Peleg," was given in memory of that event (see Deu 32:8; Act 17:26).