<p>In this study, we investigate the cosmological implications of Renyi holographic dark energy (RHDE) in the framework of Brans–Dicke (BD) theory, considering a plane symmetric Cosmological model. We consider both the Hubble horizon and the Granda-Oliveros (GO) scale as infrared (IR) cutoffs to explore the dynamical evolution of the universe. To ascertain the solutions, we depend on the premises of (i) the correlation between metric potentials and (ii) the exponential relationship between the scale factor and the scalar field. For each cutoff, we derive the corresponding field equations, analyze the behavior of key cosmological parameters such as the deceleration parameter, equation of state (EoS), and BD scalar field dynamics and discuss the conditions for accelerated expansion. The results indicate that the RHDE component exhibits negative pressure and stable behavior for suitable ranges of model parameters under both infrared cutoffs. Although the present model does not describe a dynamical transition from decelerated to accelerated expansion, it provides a mathematical and kinematical exploration of Rényi holographic dark energy in an anisotropic Brans–Dicke background. The study emphasizes the qualitative differences caused by the choice of infrared cutoff and serves as a foundation for more general theoretical investigations.</p>