"Paul" in these sentences is a
vocative; that is, the name of the person being addressed.
Traditionally vocatives are set off from the rest of the sentence by one or two commas.
"Paul, what's the matter?"
"What's the matter, Paul?
"What's the matter, Paul, are you tired?"
You may sometimes find it missing in informal communications, but technically it should be there.
(I myself may have occasionally written something like "Thank you Paul!" for emphasis, to mean "I'm glad
someone had the courage to do that!")