Is one allowed to name two of his children (of the same sex) by the same name, so that the entire Jewish name of one child is the same as that of the other?
I have never heard of any prohibition. On the other hand, it would make document authorship unwieldy (cf. Choshen Mishpat 49:7–9). And I've never heard of anyone doing so (though that may well not be for religious reasons. After all, with one exception, I've never heard of non-Jews doing it, either).