This is gonna be long but PLEASE do read, I think it would help. (I mean hopefully)
In my opinion, Youko is the title, (as in is clan, race, species.), Kurama is the name.
While recovering in the human world, he reincarnated himself inside a human baby namely Suichi Minamino. So in the human world, he was Kurama, living as Suichi Minamino. He was consciously Kurama, he remembers his past and everything, he was aware of why he was there, but to not blow his cover he lived the life of a human.
In 15 years duration of recovering his powers, Youko was deeply inside Kurama/Suichi's body, like hibernating there, but he is not recovered yet. Youko is of a different soul at the beginning, since Kurama's human body is too weak to take form or like summon Youko. it's what separates Kurama/Suichi and Youko Kurama. but It progresses during the series.
1st. Kurama vs Uraurashima in ep. 47, the Idunn Box reaches Youko Kurama through age regression as we all know, but it went too far. At the end of the battle when the smoke clears, we can hear Youko Kurama and Kurama/Suichi conversing... [DUB Youko: "Looks like my time on the outside was short. Don't ruin this, Suichi" ... "Agreed"] [SUB Youko: "The effects of the smoke are disappearing. Time is once again.." ... "Back to normal"] This transition to me looks like, Youko Kurama is letting Kurama/Suichi take control again.
2nd. Kurama Vs. Karasu He was able to reach Youko Kurama again with the help of Suzuki's item. (the potion I forgot the name). and as we all know, the potion should last for 15 mins, however, after Karasu blow Youko's plants and jumpcut, Kurama was back. In the last scene, Kurama was supposed to die, because he released a blood-sucking plant using his life energy. But he didn't because;
DUB: "every time I transform into Youko Kurama I retained some of HIS power." *'HIS' as if referring to Youko as a different person. but some of Youko's energy remains in his system. At this point, Youko Kurama was now recovered. The change begins here.
3rd: Kurama vs. Amanuma ep:83 Kurama killed a child as we all know. Well, he does understand the situation very well, there's no escape to the territory while a game is in progress, and that Amanuma is an innocent child, USED by Sensui. right before the territory blew up we saw, a very dark scene where Kurama's face was slowly getting covered in black, and his dialogue: "I have no regrets Yusuke.", was already a metaphor, that Youko is finally coming in his system. A few minutes after, Hiei said to Yusuke, "Do you think this is the first time Kurama killed a child." Let's talk about this line, There is NO WAY Kurama would kill a child during his stay in the human world, There's just no way. BUT! Youko Kurama was old and famous, surely Hiei heard stories about his ruthlessness, as to why Hiei doesn't like to fight with Kurama.
4th: VERY IMPORTANT EP. 90. Kurama can now transform into Youko Kurama at his own will. While entering the Pseudo Space, when asked, he said this to Kuwabara; [DUB: "I am not Youko Kurama, I've merely taken this form while retaining my human personality, it's a sign of increasing Demon Energy" SUB: "I"m still the person I used to be, my body has probably changed form."] The translation contradicts but, he can reach Youko now, little by little, beginning with the appearance.
Lastly in the 3 KINGS ARC, clearly shows that the two became entirely ONE. From ep 101-102. It's a person with another form, a Stronger form. Kurama was able to now live as his past self while retaining his human form.
and in ep 108, he came to a decision that he will continue his life in the human world and let go of his past. There was a sequence where we see, the form of Youko Kurama slowly detaching from him. So it's either, he let go of Youko Kurama/his demon self COMPLETELY, or he just put him on hold inside of him like before, I'm not sure.
But that's it, the recovery/progression of Kurama's character arc.