EG Save Selected with Maps
Saves selected models in a separate .max along with textures. Each texture receives a meaningful name based on the material slot.

----------What it can do----------
Saves selected objects to a new .max in the chosen folder.
Copies all used textures to the Maps folder next to the file and updates the paths. The model can be sent as an archive without lost textures.

Works with V-Ray materials (including Corona Bitmap) and Corona. Abbreviations (Diff, Refl, Opac, Illum, Disp, and others) are matched for the main slots of both renderers.
Finds textures nested in Mix, Composite, and other maps. The name follows the top-level material slot.

----------Supports groups: open, closed, and nested.
Copies V-Ray proxies and IES files of light sources.
Does not change your scene: positions, layers, materials, and texture paths return to their place after saving. In case of an error, the script also restores the scene.
After saving, it shows a report if something is not found or a slot is unrecognized.
Re-saving the same model replaces the previous textures instead of creating duplicates.

Tested on 3ds Max 2017/2023 with V-Ray 3 and Corona. In other versions, slot names may differ: an unrecognized slot will receive a CamelCase name and will appear in the report.

----------Installation----------
Close the save window if it is open and open any scene in 3ds Max.
Drag the file EG_script_Save_Select_with_Slot_Names_V2.mcr into the 3ds Max viewport. The macro will install, nothing else will happen.
Open Customize → Customize User Interface → Toolbars.
In the Category list, select EG_Scripts.
Drag the macro Save Selected with Maps (slot names) to any toolbar.
(Optional) On the Keyboard tab, assign a hotkey.

----------How to use----------

Select objects.
Click the button on the panel (it is active only when objects are selected).
Choose a folder and enter a file name. This name will be used for the texture names.
Done: a Maps folder will appear next to the .max.

P.S. If there is a problem with the script, message me, and I will fix it!