In "Star Wars: Episode IV - A New Hope," there is a memorable scene on the Death Star where Darth Vader interacts with an Imperial officer. During a briefing about the search for the Rebel base, an officer begins to speak, and Vader interrupts him with the famous line, "You are not a Jedi, and you cannot convince me otherwise." This moment illustrates Vader's authority and how he expects subordinates to communicate in a controlled and concise manner.
To directly answer your question: while there is a notable instance where Darth Vader only allows one officer to speak before reprimanding him, this does not necessarily mean he imposes a strict rule that only one officer can speak during all interactions on the Death Star. In various scenes throughout the series, different officers speak to him. However, this particular moment emphasizes Vader's dominance and the fear he instills in his subordinates, leading to a memorable portrayal of his character.