Originally Posted by luitje

I would buy them on the name in Russian passport.
If you think about the routine of getting to/out of Russia, this is the most sensible option of all.
1. Checking-in in the US: give your Russian passport to the agent. They do not care how you got to the US, but they would be keen to make sure you have paperwork to enter Russia.
2. There's no immigration control when leaving the US (unless TSA decides it doesn't have much to do and starts checking passports at the gate)
3. Russian immigration: give them your Russian passport. they don't care how you got into the US and they neither will they check your boarding card.
4. Checking-in for your return flight. Give both of your passports to the check-in agent. There are quite a few Russians travelling on two passports, so it won't be a big surprise to anyone.
5. Immigrations. Give your Russian passport. Immigration officers do not care how and if you gonna make it into your country of destination (these are you and your carrier's problems), but they do need to make sure you stayed in Russia legally. And they will need your Boarding card too. Different names on your passport and your ticket will raise questions.
5. Border Control in the US. Give your US passport to these guys. They will not need your tickets or boarding cards.