Thanks for your reply but I am not understanding your answer. My System: LR Classic 1.2, Camera Raw 14.2;
Photoshop 23.2.1; System: Mac OSX Big Sur 11.6.4.
Perhaps your answer is explicity for a Windows based system. For example I have no "Naming Template" in my Lightroom Classic > Preferences > External Tab. When I say " image exported from Lightroom Classic" I mean I clicked on the image Cmd + E and chose the "Edit a Copy with Lightroom Adjustments." option. Then the image immediately opens in PS. My LR >Preferences>External Editing page doesnt have a "Rename" box.
I solved the problem. In Lightroom Classic>Preferences>External Editing>Template, I simply chose the option "PSedit Preset." Then, for example, when I export to PS a LR image named "girl_48.jpg", and use "Save As" ( Shift + Cmd + S) in PS, the image opens back in LR as "girl_48_PSedit.psd." However when I open the same image again in PS all the editing layers, gradients, Blend Modes, Blend-If treatments are preserved and availabe for furtherr editing.