By "came up with the name", I didn't mean he invented the word "Aiki", I meant that he decided the word sounded good, and should be associated with the martial arts taught to Omoto Kyo followers. Here is a passage from and interview Stan Pranin held with Noriaki Inoue.
From this it sounds like Inoue Sensei was saying that Deguchi was the driving force behind Ueshiba calling his art "aiki" anything.
I'm not arguing that - but he didn't come up with anything, the term "Aiki" was in common in usage in Daito-ryu before that time. He just suggested they add it to the name, that's very different than conjuring it out of thin air.
Think about it, there's no way, IMO, that Takeda follows Deguchi's suggestions unless Aiki were already the core of his art.