Greases of different brand names is not the issue. The issue is that greases use different compounds as thickeners, and the different thickeners are not always compatible.
When greases made from different thickeners are mixed, the mixture may be poorer in service peformance or physical properties than either of the component products. The lessening in performance capability is called incompatibility. It may show up in any of several areas, such as (1) lower heat resistance; (2) change in consistency, usually softening; or (3) decrease in shear stability. Mixtures which show none of these changes are considered compatible.
Incompatibility is not always caused by the thickener, since each of the greases in the mixture is a complete package--thickener, fluid, and additives. Sometimes the thickener of one grease is incompatible with the fluid or the additives present in the second formulation. If the mixture proves to be significantly softer, less shear-stable, or less heat-resistant than the original grease, the mixture must be deemed incompatible.
Incompatibility is best determined in service or in service-related tests; it is not predictable. Certain thickener combinations often have been found unsatisfactory and are generally so recognized. These would include lithium and sodium greases and organo-clay and most soap greases. Tests should be run on the specific greases of interest.
The problem arises most when greases are mixed while the bearing is in service. If there is any concern about potential compatibility, thoroughly clean the bearing, race and other areas in the greased areas (including the fittings) before switching to another grease type.