Sorry, I don't know anything about the Septuagint! I know the root of Christine because I looked up the word Christ on dictionary.com and it gave me the information I gave you.
There was indeed a lot of transfer between Greek and Latin, and to an extent Germanic, Celtic, Norse and Slavic as well - they're pretty well mixed up in places. When it comes to names, Hebrew is in there as well, so names derived from all of those languages are used in nearly every European country.
But I know what you're saying about ethicity-specific names - there are certainly some out there, although it's harder to spot them in this age of eclectic naming!