Journalists

It is Lee Mortimer, and he wrote for the New York Daily Mirror. Mortimer was generally anti-Sinatra and wrote about links to the mob. Got this from Sinatra: The Life by Anthony Summers and Robbyn Swan, so it might be worth checking their Bibliography out to see what their sources were. They also write:

After years of gushing about Frank, Dorothy Kilgallen offended him in 1956 with a series of caustic articles that led off by calling him a "Jekyll and Hyde dressed in sharpie clothes." Frank raged about her at first in private, among friends. One of them, Armand Deutsch, recalled him hurling darts at a board that featured "ghastly likenesses" of three female columnists, Kilgallen, Louella Parsons and Hedda Hopper. (p.271)

Unfortunately, they don't say who these columnists wrote for but again, their Bibliography might have some clues.

Summers, A. & Swan, R. (2006), Sinatra: The Life, London: Corgi