If your sphere is a class deriving from graphics item (and it should be), and it lives in a scene (from what you said, so I assume it's QGraphicsScene) then in the constructor of the sphere set setAcceptHoverEvents( true ), and reimplement hoverEnterEvent and hoverLeaveEvent.

Something like that:
Qt Code: 
  1. class MySphere : public QGraphicsItem
  2. {
  3. public:
  4.     MySphere( QGraphicsItem* parent = 0 ) : QGraphicsItem( parent ), myName( "Not named!" )
  5.     {
  6.         this->setAcceptHoverEvents( true );
  7.     }
  8.  
  9.     void    setValues( int x, int y, int z )
  10.     {
  11.         // do something
  12.     }
  13.  
  14.     void    setName( const QString& name )
  15.     {
  16.         this->myName = name;
  17.     }
  18.  
  19. protected:
  20.     // add painting and all else you need
  21.  
  22.     void    hoverEnterEvent( QGraphicsSceneHoverEvent* event )
  23.     {
  24.         QToolTip::showText( event->screenPos(), this->myName );
  25.     }
  26.  
  27.     void    hoverLeaveEvent( QGraphicsSceneHoverEvent* event )
  28.     {
  29.         Q_UNUSED( event );
  30.  
  31.         QToolTip::hideText();
  32.     }
  33.  
  34. private:
  35.     QString myName;
  36. };
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Edit:
btw - dust on my screen is bigger than spheres on this black image