You can set the filename to be updated for Lightroom to Photoshop workflow in Lightroom Preferences > External Editing > Edit externally file naming (at bottom)
and the filename is updated in Photoshop when you save that image.
That is what I have tried. The files open in PS but not with the new name.
The name updates when you save the file in Photoshop.
Did you check the filename after saving it?
My apologies, it did save with the new name. In the past, it opened with the new name. Thank you for your help!
Glad to help