I'm not sure if this still happens, so the question may be broader, but in the Apollo transcripts the astronauts would begin a call with something like "Houston, 13". I get that they may have been on an open mic so they would want to clearly identify that they were speaking to mission control. So starting with "Houston" makes sense. But... Who else would it be other than the astronauts? Why bother saying the number, or even the spacecraft name (as in "Houston, Aquarius")?
The standard protocol for any radio communication is to specify the intended recipient and the transmitter's call sign. This practice started in the earliest days of radio. Stations were sharing a common messaging medium, so there was a need for stations to identify each other; hence the invention of call signs. Even today, ham radio operators, broadcast radio stations, and television stations must obtain a call sign (e.g. Kxxx or Wxxx) from their government.
The use of call signs continued as the military, aviation, and then spaceflight adopted the use of radio communication. Even with their own dedicated frequencies, it is useful to have a way to distinguish between individual units. Astronauts through the Apollo program all had a pilot's license, and many of them came from the military, so the use of call signs was already ingrained.
The Gemini program did not give proper names to their spacecraft (see "Why weren't Gemini capsules given names?") but instead used their mission number as their call sign. Several Gemini missions involved the rendezvous of two spacecraft. When both spacecraft were manned, it was particularly necessary to use the call signs to distinguish the recipient of a transmission.
Apollo had two spacecraft -- the command/service module and the lunar module -- so again it was necessary to use call signs to distinguish the spacecraft. Many of the Apollo astronauts were involved in the Gemini program, so the protocols had already been established. Even though Apollo spacecraft had proper names, the Gemini tradition of using mission numbers was still common.
In addition to DrSheldon’s points, it’s worth noting that the communications between Houston and the spacecraft are only one part of what each controller in mission control is hearing. Rather than shout across the mission control room, each controller wears a headset that lets them monitor multiple communications channels ("loops"). Each controller can talk with their “back room” support team, without e.g. the guidance officer being distracted by the flight surgeon’s back room discussions.
Given this many-to-many communications system, the convention of starting each conversation with “addressee, [this is] speaker” gives a listener a chance to decide if they need to listen to the rest of the message, which takes some conscious effort when listening to multiple conversations at once. While it was usually clear from the audio quality which voices were from the spacecraft, it was still helpful to hear the preamble.
It’s instructive to listen to a recording of the combined flight controllers’ audio loop from such a mission and practice tracking different conversations. The podcast The Space Above Us has two of the most famous segments of Apollo program audio, with a brief introduction to each: