There are many variants of the story of why the Hindu Kush is so called, and it's actually a pretty controversial matter. A distinct possibility is that it is actually a corruption of "Hindu Koh", meaning essentially "the mountains by the Indus". Since the name is attested relatively late (1000 CE or so; I think the story of the name referring to it as a "Hindu-killer" dates to Ibn Battuta in the mid-14th century) it is not really possible to say what the origin is; however, the use of the name "Hindush" deriving from the name of the river as a metonym for the region goes back to the 6th century BC. So it is certainly plausible that the ancient Persians would simply have called the range "the Indus Mountains".

The earliest name we can infer for the mountain range appears to be the Achaemenid Persian Uparaesanna, "above the eagle", inferred from the provincial name Paruparaesanna, "Beyond the Uparaesanna". Confusingly enough, this provincial name occurs only in Elamite and Akkadian parallel inscriptions (as well as later being used by the Greeks) - in Old Persian, the name for the province used is Gandhara for which I have not found an etymology, but I suppose it is possible that that also derives from the name of the mountain range in a local langauge. [EDIT: I see now that there's a Gandhari tribe known from the Rgveda, which is presumably the origin of the name.]

That's all I can give you on the matter, I'm afraid!