I'm not sure if it's discussed already, but I'd like to suggest a tatara_kogasa_(umbrella) tag. For when Kogasa's umbrella body seems to have a separate mind, like in post #1111103 and post #632463 or when only her umbrella is shown without her Youkai body, thus eliminating a need to create another pool.
It's sort of like the same idea that pyona is a seperate being from Moriya_Suwako.
I made a short wiki description for the tag.
Updated by S1eth