OK, let's see how this works:
1) The name reflects his/her cultural background.
Yes, because we kept their Russian names for their middle names.
2) The name is one that I've liked for a long time.
True of both their first names.
3) The name signifies a new beginning with his/her adoption.
Yes, their first names did help signify a "new beginning."
4) The name that "fits" my child perfectly.
Both first and middle names seem to fit each child perfectly, and versions of both names are common in Russian and Greek (DH is Greek).
5) you wanted to incorporate a family name
This was true of the name Christopher. It was my husband's father's name, and my husband's middle name, so it was cool to pass that on as that's definitely a Greek thing. The name Alexandra (as well as Alexander) is also very common in my husband's family. (Anybody see "My Big Fat Greek Wedding," where every other person in the "introducing the family scene" was named Nick, Nikko, Nicholas, Nikoli -- there ya go!
)
6) had to be something we both agreed on
We agreed completely -- which was both a shock, and a wonderful surprise!
This was fun, thanks, Shay!