I have wondered the same thing and came to no other conclusion than that many parents just found these name pleasant sounding.
Katya,
Tanya,
Anya,
Nadia and
Sasha contain two "a"s and a lot of people like that sound.
There also some Frisian names that sound very much like some Russian names. Sinja, Sünje, Sontje are names of Frisian origine and mean "little sun". I have never found
Sonja being mentioned as a Frisian name. But there are so many names that differ only lightly from
Sonja that I think that
Sonja could have coincidentally existed as a Frisian name before parents in that region became aware of Russian names.
The same is true for the name
Katja. There are Kaatje and other names that sound very close to
Katja and originate in Frisia.
However that does not explain why Russian diminutives became so popular all around the Western world.
This message was edited 3/7/2013, 8:21 AM