Unsupervised 3D keypoints estimation from Point Cloud Data (PCD) is a complex task, even more challenging when an object shape is deforming. As keypoints should be semantically and geometrically consistent across all the 3D frames -- each keypoint should be anchored to a specific part of the deforming shape irrespective of intrinsic and extrinsic motion. This paper presents, "SelfGeo", a self-supervised method that computes persistent 3D keypoints of non-rigid objects from arbitrary PCDs without the need of human annotations. The gist of SelfGeo is to estimate keypoints between frames that respect invariant properties of deforming bodies. Our main contribution is to enforce that keypoints deform along with the shape while keeping constant geodesic distances among them. This principle is then propagated to the design of a set of losses which minimization let emerge repeatable keypoints in specific semantic locations of the non-rigid shape. We show experimentally that the use of geodesic has a clear advantage in challenging dynamic scenes and with different classes of deforming shapes (humans and animals). Code and data will be made available upon paper acceptance.