Osler's Razor

Hillary: distinguished from Bill, for better or worse; Bernie: Bernie, Feel the Bern!, etc.,... just way more natural and fun than "Sanders"; Trump: because he has spent his entire adult life building that brand -- i.e. that's how we know him, yet don't we also know him as "The Donald"?... that said, "Trump" rings of triumph, quite naturally and beneficially so; Cruz: I think we all actually know him most commonly as "Ted Cruz"... so not sure the observation holds up; Kasich: should sooner rather than later start going by "John John", obvs
 

Aside from Hillary distinguishing herself from Bill she wants people to know she is a woman candidate. When Fiorina was in the race she was referred to as Carly. Again, I think to distinguish herself from the 16 men who were seeking the nomination along with her. And perhaps a better slogan for Cruz would be "Cruz to victory with Ted"
 

Cruz!!!!! With name like Cruz!!!! you just don't waste that kind of advantage. Cruz!!!!

Since we have known Hillary for years (Bill and Hill; HillaryCare, etc.), it seems overly formal to address her as Mrs. Clinton or Madame Secretary or just Clinton (almost disrespectful, like referring to the President as "Obama"). Hillary is our friend.

As for Bernie, he is our wonderful old avuncular Uncle Bernie. No other name would fit.
 

I love the word "avuncular."
 

In addition to what has been said (re: differentiating), I wonder if it has something to do with the different cultures of the two parties, with one being more formal/traditional than the other. I also wonder about gender politics with regard to “Hilary” (not sure about Bernie) and the differential status associated (one up and one down) with the use of familiar first names vs. more formal ways of referring to candidate (by title … by Dr. Mr., Mrs., etc.). And chicken before the egg: there is a notion that whoever defines it/you has the power; in turn, is it the campaigns doing the defining or is it their opponents/other campaigns/the media/us doing so? From the looks of it, it is a complex mix of all the above.