This is an absolutely non-political question. I’m wondering if the superficial similarity between the two words is just a coincidence. That’s what my look at Wikipedia and elsewhere on the web suggested, but perhaps someone who understands Hebrew and Arabic could say for sure.

Coincidence.  Hosanna is from the Hebrew verb yasha’ ‘to save’ (the -na is a suffix); as you can see from the AHD appendix entry on the Semitic root, it’s related to the names Joshua, Jesus, Elisha, Hosea, and Isaiah.

Husayn (often spelled Hussein), on the other hand, is a diminutive of Arabic hasan ‘good, beautiful,’ which is from this Semitic root; it’s related to the Arabic names Hasan, Husni, Ihsan, Muhsin, and Mahasin (and to the Hebrew root kh-z-n ‘strong’).