The Hebrew Bible likes to give reasons for people's names. For example, in Genesis 2:
7 then the Lord God formed the man of dust from the ground and breathed into his nostrils the breath of life, and the man became a living creature.
...
20 The man gave names to all livestock and to the birds of the heavens and to every beast of the field. But for Adam there was not found a helper fit for him.
It's not obvious in the translation, but in the original Hebrew "ground" (אֲדָמָה / 'ădâmâh) and "Adam" (אָדָם / 'âdâm, which means "man") are very similar, so people reading the Hebrew would instantly see the connection between "Adam" and "dirt".
From e-Sword (you need to download and install it on your computer):
H120
אָדָם
'âdâm
aw-dawm'
From H119; ruddy, that is, a human being (an individual or the species, mankind, etc.): - X another, + hypocrite, + common sort, X low, man (mean, of low degree), person.
H127
אֲדָמָה
'ădâmâh
ad-aw-maw'
From H119; soil (from its general redness): - country, earth, ground, husband [-man] (-ry), land.
Further along in Genesis 2:
23 Then the man said,
“This at last is bone of my bones
and flesh of my flesh;
she shall be called Woman,
because she was taken out of Man.”
[The Hebrew words for woman (ishshah) and man (ish) sound alike]
From e-Sword:
H802
נָשִׁים אִשָּׁה
'ishshâh nâshı̂ym
ish-shaw', naw-sheem'
The first form is the feminine of H376 or H582; the second form is an irregular plural; a woman (used in the same wide sense as H582).: - [adulter]ess, each, every, female, X many, + none, one, + together, wife, woman. Often unexpressed in English.
H376
אִישׁ
'ı̂ysh
eesh
Contracted for H582 (or perhaps rather from an unused root meaning to be extant); a man as an individual or a male person; often used as an adjunct to a more definite term (and in such cases frequently not expressed in translation.) : - also, another, any (man), a certain, + champion, consent, each, every (one), fellow, [foot-, husband-] man, (good-, great, mighty) man, he, high (degree), him (that is), husband, man [-kind], + none, one, people, person, + steward, what (man) soever, whoso (-ever), worthy. Compare H802.
So e-Sword gives more detail, in saying that אִשָּׁה / 'ishshâh (woman) is the feminine form of אִישׁ / 'ı̂ysh (man).
And in Genesis 3:
20 The man called his wife's name Eve, because she was the mother of all living.
[Eve sounds like the Hebrew for life-giver and resembles the word for living]
From e-Sword:
H2332
חַוָּה
chavvâh
khav-vaw'
Causative from H2331; lifegiver; Chavvah (or Eve), the first woman: - Eve.
H2416
חַי
chay
khah'ee
From H2421; alive; hence raw (flesh); fresh (plant, water, year), strong; also (as noun, especially in the feminine singular and masculine plural) life (or living thing), whether literally or figuratively: - + age, alive, appetite, (wild) beast, company, congregation, life (-time), live (-ly), living (creature, thing), maintenance, + merry, multitude, + (be) old, quick, raw, running, springing, troop.
This pattern is continued consistently throughout the Hebrew Bible, for instance in your example of Genesis 10:
25 To Eber were born two sons: the name of the one was Peleg, for in his days the earth was divided, and his brother's name was Joktan.
[Peleg means division]
From e-Sword:
H6389
פֶּלֶג
peleg
peh'-leg
The same as H6388; earthquake; Peleg, a son of Shem: - Peleg.
H6385
פָּלַג
pâlag
paw-lag'
A primitive root; to split (literally or figuratively): - divide.
So, when naming Peleg, it is saying "in his days the earth was divided", with the implication that "Peleg" is related to "divided". Again, this is obvious when read in the original Hebrew but becomes obscured in translation.
There are many good online translations with footnotes that can help you understand translation issues. e-Sword is also a good resource for this sort of thing.