If I'm referring to an event that took place in Yakutsk in 1960, should I refer to Yakutsk, USSR, or Yakutsk, Russia?
When a country's name changes, there is usually a period of time where both names are used, the new one first with some explanatory note. For example: In Sri Lanka (formerly known as Ceylon), the Prime Minister said, "Hi." Context is important, too. If your audience is very familiar with the old name, then use it, but as the name change fades into history, you have less and less need of the old name. Of course, if you're writing historical fiction set in the era of the old name, then use the old name.