We theoretically demonstrate generation of the Stokes temporal localized structure (TLS) by exploiting its Raman interaction in space and time within an optical potential well shared with another dark pulse. Excitation of the Stokes TLSs is feasible in both the normal and anomalous group-velocity dispersion regime, with a single modulated pump source. Stimulated Raman scattering constitutes influences on the stability and physical feature of the generated Stokes TLS (STLS). Particularly, breathing STLSs are also observed due to the periodic energy transfer between the primary and the Stokes fields. These findings could deepen the understanding of complex nonlinear dynamics in resonators and facilitate the excitation of different types of TLSs in potential platforms.