OT chronology and the division of the land

[Socratic Spelunker]

When did ancient hebrews name their kids? Was it at birth? Was it eight days after? The reason I ask was because the verse in Genesis that refers to him goes, "the name of one was Peleg; for in his days was the earth divided;" which I think implies that at the land was already divided at the time he got his name. If he was named at birth, then the window of time in which the event could have occurred opens a little wider.