Electroencephalography (EEG) recorded for motor-imagery (MI) brain-computer interfaces (BCIs) carries subject-identifying structure that persists across sessions, allowing separately released sessions from the same person to be linked. Existing EEG identity protections use learned or additive perturbations and operate on representations other than the covariance geometry underlying MI pipelines. We ask whether cross-session identity leakage can be suppressed directly in this covariance representation without learning a privacy model. We introduce a Riemannian transform that equalizes two subject-conditioned geometric statistics: the Riemannian mean covariance and the tangent-space scatter around it, with two optional band-specific refinements. Ablations show that mean alignment and scatter whitening carry nearly all of the suppression, while the optional stages contribute small, dataset-dependent refinements. Across two public datasets and five attackers spanning four covariance-space representations, the worst attacker falls from 90.8% to 15.6% on BCI Competition IV-2a and from 90.8% to 9.9% on OpenBMI, at a cost of 7.0 and 2.1 points of MI decoding accuracy relative to the 8-30 Hz input, and no aggregation rule exceeds chance by more than two points at any batch size. The transform requires no learned privacy model, surrogate network, or gradient-based training, and is fitted on one session and applied unchanged to a held-out later session.

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