The introduction to this subclass is succinct and funny.
Moon Shape
The third bullet point might be better worded if it was something along the lines of "you can use the bonus action granted by your Cunning Action to use Moon Shape."
I'm already imagining delightfully fun shenanigans with this feature. It's inventive. I'm having trouble figuring out the balance of it because it mostly enhances utility, but it seems fine at face value.
Beasts' Cant
This is delightful.
Moon Shape Expertise
Interesting. Your moon shape can now afford to take a hit.
I'm hesitant about this, but I think between the ability to automatically cause an attack to miss and the ability to hide in an opponents space, Moon Shape Expertise might be a little strong. Compared to other rogue subclass abilities at the same level, it offers a bit too much. My suggestion would be to cut one of the last two bullet points.
Multi-Morph
More utility, more awesomeness, more inability on my part to figure out the balance of a feature. Nothing jumps out about it to me as broken, so I think it's fine.
Moon Swarm
Well that's fun.
The boost to survivability in combination with the bonus hit points from Moon Shape Expertise makes me think this might be a bit too strong. It's right on the edge of balanced <-> too strong.
Bonus Content
Okay, that's just icing on the cake.