Andy,
Katherine is a name whose origins have always stumped me!
Concerning the "ever-pure" theory, it is probably a based on "aei" (áåß), meaning "for ever", and "kathare" (káèáñÞ) meaning clean/pure. I really suspect that all explanations pased on "kathare" are paraetymological. Moreover, I have found no record of Aikaterini written with a theta (AikaTHEerini) in medieval or contemporary Greece records . Professor
George Babiniotis of Panteion University, a well respected etymologist, adopts the Hecaterine /
Hecate connection. On the other hand,
http://www.lgpn.ox.ac.uk has no record of any Hecaterines in the classical Greek world, although the fem. names Hecataia. Hecataiae, Hecatea, Hecato, etc appear.
2.
Aikaterine is a perennial top-10 name in Greece. However, most Catherines in Greece today go by "
Katerina" which is lighter and less formal (although their ID cards do register "
Aikaterine").