I have the same problem. Up until the past month or less, Preview allowed allowed me to change the name of the file by clicking the name at the top of the window and editing it. As of recently it reverts back to the old name after I close the editing pop up. I had problems with changing the location as well. Now I have to go to File>Move... to move the file. I have tried File>Rename... and it will not rename the PDF either. I have to go to Finder, rename find the file and rename it there and then the changes immediately show in the Preview App file name.
I use preview on 3 different era's of mac, each with different MacOSX Versions due to the limitations of upgrading older macs. I am renaming up to 20-40 or more preview files a day 5 days per week for the last 7 years. This does not seem to be an intentional change in features. It seems to be a bug (like Preview not saving some annotations in the past, which is less often with more recent versions). It is only my MacBook Pro running Sequoia 15.3.1 (24D70) that has this behavior (seems to be after one the latest updates).