O'sensei studied daito-ryu and from that he created a system to teach the martial ways of the samurai, in a modern world where the samurai did not exist anymore. So the change from "jutsu" to "do" is valid, for aikido is a martial art for self-defence, self-developement and not for military purposes. It can be studied by anyone. Yet, techniqually is almost the same as daito ryu, is the goal and the purpose and the choice of not harming your attacker that was o'sensei's contribution. So, this is aikido, there is no other tradition. One can have his personal style up to a certain point (no need for another name though), but if you stray to much, it is not aikido anymore.
Morihei Ueshiba was born in 1883. The days of the "samurai" were long gone. Daito ryu was not a koryu then or now. And Morihei Ueshiba taught Daito ryu. He did not create a system. Kisshomaru Ueshiba and Koichi Tohei created a system.
Let me quote Sokaku Takeda about his definition of Daito ryu:
"The purpose of this art is not to be killed, not to be struck, not to be kicked, and we will not strike, will not kick, and will not kill. It is completely for self-defense. We can handle opponents expediently, utilizing their own power, through their own aggression. So even women and children can use it."
Morihei Ueshiba, once the most favored student of Sokaku Takeda, was only following his teacher in his own personal way. Morihei Ueshiba added his own personal spiritual ideology to create his aikido, but do not get confused -- he was a Daito ryu aiki man through and through. Nearly everything he did can be traced back to Sokaku Takeda.
It's been written that even Sokaku Takeda dabbled into some spiritual ideology and also did some mystical magical things.
Research reveals that a lot of "common knowledge" about aikido is really not all that accurate. More myth than truth.