Good to see you here Himi-cat! Missed seeing your comments in the chapter discussion! Don't know what Story Seedling's deal is with not displaying comments anymore but whatever.
Miyagi is a weird cookie
There's the TL;DR :P
But she's a responsible person, and one of the things that responsible people owners do is try and make sure that their people are healthy and happy - hence all that annoying nonsense (from Sendai's perspective) about having friends and a healthy social life and so on.
Yeah we've been seeing Sendai feeling a bit frustrated about this for awhile. Kinda feel sorry for Mio too since Sendai's always thinking about how she'd rather not be hanging out with her because she could be spending time with MIyagi instead. Then again, Mio's brought it on herself a little since she's not reading between the lines and is inviting Sendai to mixers when Sendai's got Miyagi.
It's not something silly like possessiveness being her love language - she's never experienced romantic love before this, she's never felt anything even remotely like it; as near as can be, she has no "love language".
C'mon we know Miyagi's love language is "tsun...tsuntsuntsuntsundere". :P
Agreeable with everyone else and harsh with Sendai is Miyagi's MO.
But yeah, I don't think Miyagi's possessiveness is anything out of the ordinary. Hell, Sendai might even be more possessive with the way she can feel jealous towards anything (like inanimate objects in their apartment). It's just Miyagi's way of exercising her possessiveness via "ownership" that's a bit unusual.
The idea that Sendai is experiencing such a massive wave of relief that her emotions have boiled over is going to be really hard for Miyagi to grasp, particularly since Sendai probably won't be able to explain it - she'd need to say words to the effect of "I'm just so overwhelmingly happy that you did something like this to show how much you love me", and that would be totally breaking the rules
Oh have you met the Sendai that pops up in my daydreams from time to time? She's able to passionately express her feelings and Miyagi lovingly reciprocates them.
But the story would've been over in a few dozen chapters if it went the way I daydream about it.
One thing that's interesting to see, though: Miyagi seems to have laid claim to Sendai's name. The moon and the leaf, marks of her possession of Sendai's very being, even down to her name - I'm guessing we'll see a whole lot more of "Hazuki", particularly when they're alone together. Whether Sendai will be allowed to take possession of Miyagi's name remains to be seen.... though Miyagi is a sucker for arguments from fairness, and Sendai...er, Hazuki... is a right sneaky one who's very good at figuring out how to get her way....
Ya I have a feeling they're going to keep using their family names except when they're alone. And inevitably Miyagi will put up a bit of resistance against Sendai addressing her as "Shiori" but Sendai will eventually get her way.