I’ve never read the old testament all the way through, but one thing I did notice in what I have read, is that I couldn’t find any name used for more than one person. That is, through hundreds of pages and (possibly) thousands of characters or just people mentioned, it seems as though each one had their own unique name. Just off the top of my head, I know that in the new testament there were at least two Johns; John the Baptist and John the Disciple. But, does that work out in the old testament?
Trying to think of some, all I could come up with off the top of my head were names where there was someone in the OT with the same name as someone in the NT (like Saul and Joseph). Not what you’re looking for, though.
In general, the practise of naming people after people seems to have become prevalent some time after the Babylonian Exile in the 6th century BC and before the Maccabean Revolt in the 160’s BC (start reading at Chapter 2 and you find half a dozen in the first few verses)
Not sure I can narrow it down further than that. There seem to be two Jeshua’s in Ezra (one contempory at 2:2, one historical at 2:40 also mentioned in 1 Chron 24) - there may be some other isolated examples, but nobody famous.
There’s a Noah and a Noa in the Hebrew Bible. Noa is female; Noah built the ark.
Not quite the same name, but close.
Therre are quite a few duplicates among king names, either Israel and Judah each having a king with the same name or a couple of cases (Jeroboam I and II, for example) where two kings of the same kingdom had duplicate names.
The name Yehoshua. varopis;u remdered Joshua, Jeshua, and Jesus, includes: 1. J. ben Nun, the military leader of the invasion of Canaan, 2. the high priest after the return from the Babylonian Exile. 3.J. ben Sirach, the author of the deuterocanonical book of Ecclesiasticus, and of course the NT Messiah.
There are doublets scattered through the various genealogies, though none come quickly to mind. The descendants of Cain include several names that are dialectal doublets of Seth’s descedants.
People are always careful in any work of fiction to avoid duplicating character names. 
Given the blatant self-contradictions in Genesis, I think we can exclude any expectation of that level of editing.
Dragging this somewhere back to within a stadia of the topic, what’s the current scholarly explanation for the oddities in Genesis? Were two distinct creation myths conflated?
Either that, or two distinct account of what was probably the same underlying creation myth.
There appear to be two Zacharias 's, and Jesus confuses the two in a story he tells in the New Testament.
There are four people named Enoch in the bible. The first is one of Cain’s sons, who built the first city. The second is Noah’s great-grandfather, who disappeared into heaven. The third is one of the sons of Reuben, and the fourth is one of the sons of Midian.
There are two Sauls, the first a son of of Simeon, and the second the first king of Israel.
There are three Gershons. The first is a son of Levi. The second is a son of Moses. The third is one of the people who came back from the Babylonian captivity.
There are 15 Jonathans. The first is one of the sons of the second Gershon. The second is the son of King Saul. The third is a son of Abithar. The fourth is one of King David’s nephews. The fifth is one of David’s warriors. The sixth is the son of Jada and brother to Jether (a member of the tribe of Judah). The seventh is the person David put in charge of storehouses outside of Jerusalem. The eighth is one of David’s uncles. The ninth is somebody who came back with Ezra from the Babylonian captivity. The tenth is somebody else who came back with Ezra who disagreed with Ezra’s order to force the returnees to divorce their foreign wives. The eleventh was a Levite who returned from captivity. The twelfth is a head of a priestly family at the time of the return. The thirteenth is the father of one of the men who played a musical instrument in Jerusalem after Ezra and Nehemiah rebuilt the wall, the fourteenth is a secretary who was one of the people who imprisoned the prophet Jeremiah, and the fifteenth is an army general who served the Babylonian governor of Judah.
I’m sure there are more cases of repeats of biblical names.
More seriously, how about Mary, a name that has caused endless confusion because of multiple vague references.
http://en.allexperts.com/q/Bible-Studies-1654/Mary-bible.htm
Also check out this very long answer on James.
ETA: Whoops. Sorry, I forgot that the OP specified old testament. I’ll let my answer stand because the link goes to a site that may answer some of these questions.