Magento 2: How to get current admin user detail?

you need to add this to the constructor of your class

protected $authSession;
public function __construct(
    ....
    \Magento\Backend\Model\Auth\Session $authSession, 
    ....
) {
    ....
    $this->authSession = $authSession;
    ....
}

Then create this method

public function getCurrentUser()
{
    return $this->authSession->getUser();
}

this will give you the current logged in admin.
You can later get the details like $user->getUsername() or $user->getEmail().

How to get current admin user detail?

inject backend session in your controller

public function __construct(
....
\Magento\Backend\Model\Auth\Session $authSession, 
  ....
 ) {
  ....
   $this->authSession = $authSession;
   ....

}

and use this to get user name or email

 $this->authSession->getUser()->getUsername();
$this->authSession->getUser()->getEmail();

Your Controller already extends \Magento\Backend\App\Action so it already has the authorization object. No additional injections are needed. To get the user simply use this function:

    /** @var \Magento\User\Model\User $user*/
    $user = $this->_auth->getUser();

Other answers are suggesting duplicate injections, which are not needed.