Shear rheology is a fundamental property of soft matter, which can be deformed. Although the shear rheology of fluids has been well studied at the macroscopic scale, understanding the microscopic processes of rheology at the single-particle level remains a challenging issue. Dusty plasma serves as an ideal platform for exploring microscopic dynamics of system at the individual particle level. Here, we study the shear rheology of confined double rings of strongly coupled dust particles in a dusty plasma. The outer ring is actively driven to rotate using laser illumination. Depending on the particle number, the inner ring may passively rotate following the outer ring at different angular speeds, resulting in shear rheology. The number of dust particles influences particle arrangement, which is characterized by the pair correlation function, bond-orientational order parameter, and triangle skewness. That further alters structural stability, significantly affecting the shear rheology.