Why is Hiiro a Nora?
She's first named by his father (the "sorcerer" is mentioned as her true master in the wiki so I suppose that means he named her first) as Mizuchi and then his father let Yato name her as Hiiro.

I think she never tainted Yato  because she cares for Yato so much that she never did anything a regalia shouldn't do to taint their master.

I haven't read that far in the manga so I can only suspect that the sorcerer allows her to be named by others for some sinister plan against the heavens.

http://noragami.wikia.com/wiki/Nora