What is the significance of Judas's name? The Old Testament has a question hanging over it: "Who will inherit the promises to Abraham?". Isaac is chosen over Ishmael, Jacob over Esau and (though in one sense all the sons of Jacob inherit) Judah is chosen over his brothers. Likewise Perez over Zerah and so on through the line of David.

There is a parallel theme of a 'remnant' surviving God's judgement on disobedient Israel, and the survival of Judah when Ephraim is destroyed is part of that theme. Though Judah is eventually sent into exile, it is the remnant of Judah that returns and Judah's line that ultimately leads to Jesus (though not through a human father).

In that light, what is the significance that the one disciple who betrays Jesus is named Judas (the Greek for Judah)? Is the intention to highlight that the old cycle of rebellion, judgement, 'repentance' and relenting has finally come to an end?
As you already stated, Judas (Strong's g2455) is simply a variation of the name Judah. Iscariot (Strong's g2469) translates to "man of Kerioth." Kerioth is one of the cities listed in Joshua chapter 15 as the allotment of the Promised Land for the tribe of Judah. So there doesn't seem to be a literal meaning behind the name, other than likely belonging to the tribe of Judah. 
As for a non-literal significance, there is certainly a parallelism between Israel (and the kings of Judah in particular) rebelling and Judas-Iscariot betraying Jesus. Whether or not this parallelism has a further significance, I can't say.