What happened is that Cesium launched a product called “Cesium OSM Buildings”. The original OSM Buildings is understandably unhappy about that because they have been using the name for years and this move by Cesium, a much larger player, is now causing confusion and harming their visibility.
The OSMF was only involved because Cesium has asked us whether it was ok to use “OSM” like that. But the OSMF only checks whether a name violates OSM’s trademarks. We don’t check whether a name violates someone else’s trademarks. (Maybe we should? But it would certainly be a policy change for the OSMF to start arbitrating disputes between companies using OSM data.)
(Note that I didn’t participate in this decision of the OSMF board of directors, even though I was already on the board at the time. I have an obvious conflict of interest, as both Cesium and OSM Buildings are technically competitors of my own OSM2World project.)