Production Studio
Paramount Studios
Vertigo was produced by Paramount Studios—you know, the guys with the mountain logo. Founded in 1912 as the Famous Players Film Company, Paramount's now the longest running movie studio in Hollywood.
In the 1950s, Hitchcock was Paramount's hot property. They gave him complete say over any project under $3 million—casting, story selection, screenplay, editing, and publicity—and also gave him the rights to several of his films once they were released. All this led one Paramount exec to say that "Paramount functions practically as a studio setup for him" (source).
Vertigo would be the last film Hitch made with Paramount. He'd done 4 others: Rear Window (1954), To Catch a Thief (1955), The Trouble with Harry (1955), and The Man Who Knew Too Much (1956), all—except for Harry—huge successes for the studio. Paramount objected to the content of Hitchcock's proposal for Psycho, so he eventually filmed it at Universal Studios and Paramount simply distributed it. That's why you can see the Bates Motel on the Universal Studios tour.
The film's story comes from a French thriller by two authors Hitchcock admired. Some conflicts arose during the adaptation process (see our "Screenwriters" section for the story), and the disagreements were complicated by Hitchcock's health problems, which took him away from the screenwriting process at several key points (source). There were also few points of contention between the studio and Hitchcock during film production. Check out our "Modes of Production" section for more on that.