Does the NYT style book apply to the Crossword? Since it's Mr. Loaf, maybe it must be The Edge.
In another Times controversy, seems they can't decide if it's Burma or Myanmar--headlines tend to use Burma/Burmese, but article text seems to favor Myanmar.
NYT style applies to crossword clues, but not answers -- after all, there's no capitalization or punctuation in the grid itself.
Once again, third person requires the definite article; second person does not.
I would lean towards including the article at all times, as there used to be a professional wrestler named "Edge". If Edge and The Edge were in a social setting, I feel like it would be a faux pas to call out "Hey, Edge!" when referring to Adam Clayton, where a simple "Hey, The Edge!" could avoid that unseemly scenario.
If you called out "Hey, Edge!" when referring to Adam Clayton, that would indeed be a faux pas, as you'd have one pissed-off bassist on your hands.
Look, if you're going to cover obscure bands like this, you can't expect those of us outside your little indie hipster circle to know all the trivia.
The United States States Department still refers to it as the Union of Burma and notes on their profile web page for the country that the US government overall uses Burma, for what it's worth.
As evidenced in tonight's SOTU.