An addon to automate the naming of meshes.
Tested on Blender 3.0.0
Installation
Download quick_mesh_rename.py from the releases. Open Blender, go to the addons in your user preferences, and click install. Select the file and then enable the addon.
Usage
Click the mesh icon in the outliner bar.
The addon will go through every object and rename the mesh associated with it. If a mesh is used by multiple objects, it will only be named the first time it is encountered.