Does it really matter?If we called it the' Ministry of Military affairs' it would still essentially be Partisan Politicos second guessing trained,experienced Military staff Officers to ensure that H.M. Armed Forces 'keeps'on message',ensures HMG looks good to the masses,and does so as cheaply as possible.Any side effects such as 'defence of the realm',external/internal security etc.,seem to be simply expected not planned or paid for,after all" we've got the best Army in the world,they'll sort something out!"
There was in fact a "War Office" up till 1964, when it was amalgamated with the Ministry of Defence, the Admiralty and the Air Ministry to form the current MoD. Curiously though, the first 'Defence Minister' was Winston Churchill who gave himself the post during WW2 even though there wasn't a Defence Ministry till shortly after the war.
Following the war office/mod logic ....
we could rename the Department for Work and Pensions as the Office for feckless scroungers and old folk dying of Cold
OR UK Border agency as Office for letting foreigners into the country to murder rape scrounge and whine they are being disrespected/racially abused.