The combination of strong spin-orbit coupling and strong correlations holds tremendous potential for interesting physical phenomena as well as applications in spintronics and quantum computation. In this context, we here study the interplay between the Rashba spin-orbit coupling (RSOC) and the Kondo screening in noncentrosymmetric f-electron materials. We show that the Kondo coupling of the f electrons becomes anisotropic at high temperatures due to the RSOC. However, an isotropic Kondo effect is restored at low temperature, which leads to a complete Kondo screening. We furthermore demonstrate that the Kondo effect has influence on the Rashba splitting in the band structure, which becomes temperature dependent. Although the f electrons are localized at high temperature, a helical spin polarization of the conduction band emerges due to the scattering with the f electrons. With decreasing temperature, the Kondo screening occurs, which leads to drastic changes in the band structure. Remarkably, these changes in the band structure depend on the helical spin polarization. For strong RSOC, we observe that the hybridization gap of one of the helical bands is closed at low temperature and a helical half metal is formed.