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Aviv and Shai would fit in no problem, some people might pronounce Shai like Shay but I don't think it would be a constant problem.
Rotem on the other hand might raise some questions on where it's from and how you pronounce it and such. I'm not sure how to pronounce it either but I assume most english-speakers (at least in the US) would pronounce it like 'row-dum' or 'raw-dum'. It's not really all that strange however, just a little bit peculiar.