Remote sensing (RS) applications increasingly operate over distributed infrastructures that integrate space-airground- sea resources with edge intelligence, yet remains challenging to centralize due to geographic dispersion, cross-institution barriers and privacy regulations. Federated learning (FL), a promising privacy-preserving distributed learning paradigm, has garnered wide attention. However, the practical application of FL for RS encounters the issue of label noise stemming from inevitable annotation errors. In this work, we pioneer an early investigation of label noise in distributed RS tasks. We introduce the Federated Representation Optimal Matching (FedROM) framework, which guides robust representation alignment in the presence of noisy labels without requiring auxiliary data or transmitting extra sensitive information. Specifically, FedROM focuses on the robust local updating process, where clients first identify underlying noisy samples from the perspectives of both per-sample loss value and latent representation space. Subsequently, inspired by the optimal transport technique, we adaptively align the latent representations of identified noisy samples with their corresponding closest class centroids with the least representation matching distance, where class centroids are averaged by the latent representations of other relatively clean samples. This reduces the misleading effects caused by noisy samples and guides the model to capture more robust semantic features in the latent representation space. Theoretical analysis proves the robustness and convergence of FedROM. Extensive experiments on two real-world distributed RS datasets covering multi-source domains and varying label noise rates demonstrate the robustness of FedROM against eighteen baseline methods. Meanwhile, FedROM also surpasses its counterparts in conditions of no label noise, narrowing the gap with the centralized training. To facilitate related communities, our code is open-sourced athttps://github.com/Sprinter1999/ROM.