Burma? Myanmar? Yangon? Rangoon? It's more than 'potato, potaahto...'

H.D.S. Greenway in The Boston Globe devotes a column ("Playing the Name Game") to how different publications work with the names of places that are more familiar in their previous name incarnations. Do you correct a source? Do you explain? Do you describe the political implications, if any, that might adhere to one of the names?