<p>This paper extends the proximal point method to solve difference of convex (DC) composite problems in Hadamard manifolds. We consider the problem of finding a critical point of a function expressed as the sum of two (non-convex and non-differentiable) DC functions. The proposed method uses only the first convex component of one DC function in the proximal term, incorporating the subdifferential of the other convex components in the regularization term. This approach simplifies each iterate to solving a strongly convex subproblem. We prove that any cluster point of the sequence generated by the method is a critical point of the objective function. Additionally, we present an alternative version using quasi-distances for regularization in the Euclidean context, showing that it retains the convergence properties of the classical method. To our knowledge, this is the first study of the proximal point method for DC composite problems in both Euclidean and Riemannian contexts, offering new insights and potential applications in various fields.</p>