One question: why aren’t all the stories simply using Alex Lifeson as his name?

Because his name isn't Lifeson.

Those who choose a different stage name do it for a lot of reasons, and sometimes one of them is the ability to have an additional layer of anonymity in real life. When the police blotter in Naples, Florida says "Alex Zivojinovich", there's the hopeful chance that maybe it won't get reported on CNN because not everyone makes the connection. Clearly that didn't work this time, but the point is that he chooses to be famous under a fake name and to live his daily life under his given name.

Now, Sting is a different story... he says his own mother calls him Sting.