Officially, Kakashi gave away his Hokage status to Obito as it was always Obito's dream, instead becoming his right hand...
Unofficially though, they are both recognised and named as Hokage as most villagers argue that they are not whole without each other.
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Obito x Kakashi Headcanons!
FanfictionWell, title says everything. ^^" This is basically fandoms headcanon about ObiKaka relationship! (Headcanon = word describing something that hasn't happened in original canon but has happened in someone's head)