To ensure consistent naming of exported atlases in Unity, you can use the "Atlas per skeleton" option during export. This will name each atlas after the skeleton, matching the name of the corresponding skeleton data file. If you want to customize the names further, you can use the command line interface to specify a name for the atlas during export. Additionally, organizing your images into subfolders and using a pack.json file can help manage how images are packed into atlases, allowing for more control over the naming and structure of your exported files.

chow Spinebot's answer above is not wrong, but in this case what you want to name is the file name of the texture atlas "page" rather than the atlas file name, which there is no way to specify before exporting. After exporting, it is possible to rename them by manually editing both the page image file name and the page image name as described in the atlas file.
Or are you concerned with the _Material suffix or lack thereof depending on page count?

chow Please do not rename the primary generated Materials, this might cause problems with spine-unity's automatic asset import pipeline, e.g. upon Reimport. If you want a different material name after exporting, you have to rename the atlas textures, as well as the atlas texture name in the .atlas.txt file.

@chow Sorry, I just noticed I have misunderstood that you likely want to unify _Material vs _cg1 to the same suffix. You could comment out the following line in the source code to uniformly receive the page-name like _cg1 instead of _Material:
EsotericSoftware/spine-runtimesblob/4.2/spine-unity/Assets/Spine/Editor/spine-unity/Editor/Utility/AssetUtility.cs#L690-L691