It's not nearly as clear cut as that.
It was called "Aikido" from 1942.
Morihiro Saito stated quite repeatedly that what he was shown by Ueshiba in the 1960's was closest to what appears in the 1938 manual "Budo" - somewhat different than what Kisshomaru and Tohei were showing in Tokyo.
Anyway, he didn't actually chose the name - it was chosen by committee at the Dai Nihon Butokukai, although he did choose to stick with it later.
Kisshomaru always cited the key revelations behind Aikido as occurring in 1925.
The old ways of Budo? Here's a quick and famous quote - "Strategies for war become strategies for peace". Can you name the year? If you can, then what does that do to your pre-war/post-war dichotomy?
I was quite sure 'Aikido' was given that name in 1942 (something to do with excluding it from a pro-war category, alongside other martial arts?)