Hearing that name always caused a great ache inside Naruto. Kurama braced for impact, as he was the one most affected by these emotional currents within Naruto. Being inside a human offered a far larger emotional landscape than what a Tailed Beast could conjure up on its own. In fact, it was this level of anatomical empathy that allowed Kurama to mature from his days of pure wrath and chaos—to experience the humanity of mankind.
He wished for every Tailed Beast to be held in a human heart, for it was a completely different world in here.
For example, the pain and sense of loss that gushed through Naruto when he heard the word "Jiraiya"—Kurama felt it first-hand. It was an experience no Tailed Beast could muster on their own. They simply did not possess the capability to feel so deeply. Yet, being inside a human, it was fair to say a Tailed Beast might have gained more than the Jinchūriki host.
To be human was something far more important than chakra itself. Kurama believed this human feeling was more primordial than chakra, and that chakra manifested into this world as a result of that humanness.
The beast wondered if there would come a time in the near future when he'd be alone again, with no host. At that point, would he be able to sustain or feel all these emotions he currently had access to? Would he be able to retain this humanness—this empathy? Would he still be a beast?
The very thought gave him some idea of what the future might be. For the thought of being alone again, without a host, was to lose Naruto. That feeling brought a great sense of loss in him, accompanied by pain and sadness. And in that moment, Kurama realized he'd never be the same again. Every day he spent with this boy, he was growing into a beast that could also feel like a man—though slowly as it may be.
This brought him a sense of peace, although it was engulfed by the sense of loss he felt for Naruto.
For the very first time, such human emotions were being transferred from Kurama to Naruto. Where normally it had been rage and revenge, Kurama now exhibited love and hope—and Naruto felt them all the same.
"You okay there?" asked Naruto.
"It sure has been a pleasure, Naruto," said Kurama, with gratitude.