Renaming a material isn't reflected in the Static Mesh Editor until it is closed and reopened.
Let's have imported static mesh with material. Then select material using "Browse to asset" button. Rename (using F2) and return to Static Mesh editor. As you can see, the name of material didn't change and using "Use selected asset" doesn't do anything (I believe this is because internal reference to material is correct, only name is not updated). Closing and reopening Static Mesh editor solves this issue (name is now loaded correctly).
1. Open a new blank project (with Starter Content)
2. Content Browser > StarterContent > Open the "Shape_Cube" static mesh
3. Details panel > Material > Material Slots > Select the magnifying glass to quickly find the material
4. In the Content Browser, rename the material
5. Go back to the open Static Mesh Editor & look at the material name
Results: The material name will still be the old name until the Static Mesh Editor is closed and reopened
Expected: For the material name to update with the new name as the rename takes place
Head over to the existingAnswerHub thread and let us know what's up.