This following solution will not help you retrieve the filenames which were already removed from the trash, before implementing my solution. However you can use this solution to retrieve the filenames removed from the trash, in the future if you need to.
This AppleScript code works for me using the latest version of macOS Mojave.
You can attach a "Removing Items From" folder action to the /Users/YOUR SHORT NAME/.Trash folder that will write to file, the names of the files that were removed from the trash.
Create a new Script Editor document and insert this following AppleScript code.
on removing folder items from theFolder after losing removedItemNames
writeToTheFile(removedItemNames)
end removing folder items from
on writeToTheFile(removedItemNames)
set theFile to POSIX path of (((path to desktop as text) & "Removed From Trash.txt") as text)
set text item delimiters to linefeed
set theText to (removedItemNames as text)
try
set writeToFile to open for access theFile with write permission
write theText & linefeed to writeToFile as text starting at eof
close access theFile
on error errMsg number errNum
close access theFile
set writeToFile to open for access theFile with write permission
write theText & linefeed to writeToFile as text starting at eof
close access theFile
end try
end writeToTheFile
Next, save your new Script Editor document as "Removed From Trash Folder Action.scpt" to the folder... "/Users/YOUR SHORT NAME/Library/Workflows/Applications/Folder Actions/". Saving it to that location will add it to the list of scripts you can attach to folders in the Folder Actions Setup, which can be accessed when right clicking a folder in Finder, in the Services contextual menu.
Before you will be able to attach a folder action to the Trash folder, because the Trash folder is "hidden", you will first need to run this following AppleScript code to unhide all hidden files.
do shell script "defaults write com.apple.finder AppleShowAllFiles TRUE
killall Finder"
After all is said and done, if you want to re-hide all originally hidden files, just run this following AppleScript code to hide all hidden files.
do shell script "defaults write com.apple.finder AppleShowAllFiles FALSE
killall Finder"
Here is a look at the Folder Action creating the text file with the names of removed files from the trash
