Fritz Lang and friend
 
The record seems clear on this point. Fritz Lang loved monkeys, and especially toy monkey dolls that he could pretend were his constant companions. The best-known of the succession of toy monkeys was called Peter, but possibly all of them were called Peter, it’s not really clear.

Here’s some testimony on the subject, courtesy of Fritz Lang. His Life and Work: Photographs and Documents, edited by Rolf Aurich, Wolfgang Jacobsen, and Cornelius Schnauber:
 

Lang had a rather touchingly tender, sentimentally boyish relationship to Peter the Monkey: he took him with him on trips, put him to bed, dressed him up and posed in pictures with him. In the countless letters he exchanged with his lifelong friend Eleanor Rose, there are many passages devoted to Peter: for example, greetings from him for Magali, Eleanor Rose’s favorite cat; or letters directly addressed to Peter or “written” by Peter to Eleanor:

“Peter sends his warmest regards. He is meditating a great deal and enjoying the California sun. He loves martinis, smokes a long pipe now and again, and has taken to chewing gum. He sends his compliments to Magali and wishes her the best.”—Fritz Lang to Eleanor Rose, July 30, 1963

 
I found that quotation from this “Old Hollywood” blog—there’s slightly more on the subject there, so be sure to check it out.
 

Fritz Lang and Peter the Monkey at home, c. 1960’s
 

As you can see from the quotation, Peter the Monkey favored martinis, according to Lang. In fact, Peter liked to have them for breakfast. Well-known Hollywood biographer Charlotte Chandler, author of books on Groucho Marx, Alfred Hitchcock, Mae West, Billy Wilder, Bette Davis, etc., had first-person experience with Lang’s morning repasts:
 

It was his favorite breakfast—scrambled eggs with martinis. Or rather, martinis with scrambled eggs. It was a breakfast he preferred, and he preferred not to eat it too early in the morning. There were scrambled eggs for two, Fritz and me, and two martinis—one for Fritz and one for Peter, who was sitting at the table with us. Peter was a German felt monkey doll who wore his sailor cap at a rakish angle, a turtleneck sweater, a gold earring in one ear, and a suave, urbane look on his face that indicated he knew Hamburg’s St. Pauli district well. Fritz always ordered a martini for Peter, who was his mascot and alter ego. Then he helped Peter drink it.

 
(For those puzzled about the biography of Lang that Chandler never wrote, her account appears in the Anthology Film Archives book Fritz Lang 2000, edited by Robert Haller.)

Here’s Lang being interviewed by William Friedkin in 1975:
 

Previously on Dangerous Minds:
Tales of the Unexpected: William Friedkin interviews Fritz Lang
Fantastic explanations of the movie trickery in Fritz Lang’s ‘Metropolis,’ 1927