Glad you are enjoying Tsukimichi! The first season of the show in particular did a lot of trimming and rearranging of the source to better fit a seasonal anime structure. They basically cut out all of the other POVs (the other heroes) from the first season and moved it into the second season.

If memory serves, granting of a name gives those under a ruling contract more power. Also, if the name is closely aligned with the personality/abilities of the named, then it kind of synergizes and provides more of a boost. This is an idea that was kind of introduced into the story, but hasn't really been heavily explored or expanded as the story has gone on. If you find the mechanic interesting, then a very similar thing is done in Reincarnated as a Slime where it is much more fundamental and fleshed out.

The idea of "true names" is a very ancient one in mythology and literature. Based on the wiki page, it looks like it goes all they way back to Egyptian mythology. Off the top of my head, it is a feature in an epic like The Odyssey by Homer as well as a fairy tale like Rumpelstiltskin.

Getting back to Reincarnated as a Slime, lots of people like to compare Tsukimichi and Slime. The two series bear a lot of similarities in their worldbuilding and mechanics (naming being one of them). Slime was published later, but adapted into anime first, but they do tend to draw inspiration from one another.