Kevin Brooks in his Jews of Kazaria mentions that they like to give names associated with holidays like Pesach, for example. So do the Mountain Jews who might be the missing link in all this. If my theory is correct and the Kazars were of Israelite origins to begin with then the Mountain Jews who are their descendents and the Pashtun tribes of Israelite origin should have similar names. In countries untouched by mass media naming is very conservative (no Tiffanys and Brittanys) so this might be worthwhile to study. Even though the Chanuka story took place much after the loss of the ten tribes there may have been an earlier seasonal holiday from which the name came. There's a group at Bar Ilan University that studies names.
The tradition is that the Jews were redeemed from Egypt because they kept their Hebrew language, their traditional clothes and their Hebrew names. Maybe in the merit of keeping their names they will have redemption.