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Gene Roddenberry had a war buddy named Kim Noonien Singh. He named Khan after him to see if he could find the man he lost contact with. Noonien Soong was named for the same reason. That's the real-life reason...no canon reason exists although since we learn Noonien Soong's ancestor Arik reorganized the Augments we can presume that his family was proud of his accomplishments and named their descendants after him (remember though that Khan was around 200 years before Arik Soong. He didn't invent Augments, he just brought them back to life). Presumably human society has progressed to the point where naming a kid after a brutal warlord doesn't preclude them from getting personalized cakes for their birthday.

Nuclear weapons were not particularly useful against shields in the 24th century. The Borg had much more powerful weapons at their disposal.