Now considering the context of the Cold War, Fleming's job and inspiration, wouldn't it just be a tad logical for Dr. No's name to be inspired by this?
Dr. No was inspired by (Dr.) Fu Manchu. Of the name, Fleming once wrote "I've always been inclined to say no, it's a shorter word than yes and it commits you less." I think he was just looking for a short simple name like 'Dr. Fu.'
Interestingly enough, Fu Manchu was played by Christopher Lee sometime in the 60s. Lee is Fleming's cousin and as you are no doubt aware, he played Scaramanga in The Man with the Golden Gun. So if you ever wanted to see what a possible Christopher Lee as Dr. Julius No would look like, go see The Face of Fu Manchu.