It's time for an Inulysis!
InuYasha - Yashahime Analysis
In Yashahime: Princess Half-Demon Episode 22 "The Stolen Seal" We see a flashback of the Inu no Taishou and Kirinmaru destroying a shard of the Grim Comet that took place 500 years ago. After destroying the shard, Zero gives thanks to Taishou. Taishou says he will return to the Western domain and says Farewell, Zero begins to talk.
"Taishou. Sometimes, I ask myself how long we must continue this."
“I wonder. We are fated to journey an endless path. Who knows where it will take us?"
Zero responds: "Do you think we will have to welcome the end of day?"
Taishou Answers with: "No matter where this leads us, or what sort of end greets us… You are who you are, Lady Zero. I would like for you to remain that way.”
Taishou leaps into the sky as he leaves. Zero says to herself: "I am who I am, you say... I will honor your advice."
This speech parallels what Towa tells Riku in Yashahime: Princess Half-Demon Episode 21 – "Secret of the Rainbow Pearls" Riku responds to Towa the same way that Zero does to Taishou.
Here, Taishou addresses Zero with the -dono honorific. It is even more respectful than -san; the effect in modern-day Japanese conversation would be along the lines of “Milord So-and-So.” Originally, tono 殿, with a to と, was used to refer to the "mansion" where a lord lived, then later, it started being used to refer to the feudal "lord" himself. In the Heian period (794–1185), the “dono” honorific was attached to names to people of importance, public officials, but during the Kamakura period (1185–1333), the honorific had lost its original value, and the “sama” honorific, considered more respectful, used instead.
Since dono 殿 no longer had the value to refer to people of importance, it started being used toward less important people. Such as, soldiers in the military, samurai, and so on. We usually see the dono honorific being used in manga and anime series that are mostly revolved around a historical time period, with samurai or ninjas or if the character is speaking as though they are from a different time period themselves, and so on.
This matches up nicely, as according to the timeline, this takes place in the Heian Period. Making Taishou's "dono" honorific usage, accurate to the time period.
Sources: - Official Manga Honorific Guide - https://www.japanesewithanime.com/2016/07/dono-honorific.html