Tom Hagen is never called anything but "Tom" in Parts 1 and 2. Never Thomas or Tommy. It's about 150 times, including stage directions, per Geoff's transcripts. In the novel, he's called "Thomas" the very first time he's named by the narrator, and then called Tom every time thereafter, including in all dialogue.

Tom is referred to as "Tom Hagen" at times when it seems unnecessary, e.g., "Tom Hagen is no longer consigliere," when he's present and everyone in the room knows him. In the movie, Kay got, "...something for your mother, and for Sonny, and a tie for um um Freddy, and Tom Hagen got the Reynolds pen..." That can only reflect how Michael
habitually refers to him. The narrator in the novel runs amok with this, often calling him "Tom Hagen" multiple times in quick succession. In the section where Tom is arranging for Lucy to go to Las Vegas, Puzo calls him Tom Hagen in three consecutive sentences.