The Security Service has had a variety of names, most famously MI5, since it was established in 1909. This has often led to confusion about what the Service has been called at various points in its history.
The Security Service is founded as the Home Section of the Secret Service Bureau, under Captain Vernon Kell. (See "The establishment of the Secret Service Bureau"). It is placed under the nominal supervision of the Directorate of Military Operations of the War Office, the predecessor of today's Ministry of Defence. The branch of the DMO responsible for the Secret Service Bureau is called MO5.
The Secret Service Bureau is absorbed into the War Office for the duration of the war. It becomes part of section 5 of the Directorate of Military Operations and is given the name MO5(g).
MO5(g) is moved across to the newly established Directorate of Military Intelligence within the War Office. It becomes section 5 of the Directorate of Military Intelligence - hence MI5.
MI5 is renamed as the Defence Security Service.
The Defence Security Service becomes the Security Service, the name by which it is still known today. However, "MI5" is still widely used as a short alternative to our official name.