Move files and create unique name something wrong with my script

Question

Can you see where I might be going wrong here?
Just trying to create a unique name if something exists.
In English.
Move file to the destinationFolder
Item exists in destinationFolder > Move file in the destination folder to the fake Trash > If it exists in fakeTrash too then give it a new name an ending of_a.psd then out it in the trash
Once thats done move start file to the destination folder.
Currently when the file exists in the destination folder and in the trash, I get the prompt then the error
error "System Events got an error: Can’t get disk item \"NN_FR10WW06290PK3LE.psd\"." number -1728 from disk item "NN_FR10WW06290PK3LE.psd"
set fileMatrix to {¬
          {folderName:"BHS", prefixes:{"BH", "SM", "AL"}}, ¬
          {folderName:"Bu", prefixes:{"BU"}}, ¬
          {folderName:"Da", prefixes:{"ES"}}, ¬
          {folderName:"Di", prefixes:{"DV"}}, ¬
          {folderName:"Do", prefixes:{"DJ", "RA"}}, ¬
          {folderName:"In", prefixes:{"GT", "CC"}}, ¬
          {folderName:"Fr", prefixes:{"FR"}}, ¬
          {folderName:"No", prefixes:{"NN"}}, ¬
          {folderName:"Ma", prefixes:{"MA", "MF", "FI", "MC", "MH", "MB"}}, ¬
          {folderName:"Pr", prefixes:{"PR"}}, ¬
          {folderName:"To", prefixes:{"TM15", "TM11", "TM17"}}, ¬
          {folderName:"Wa", prefixes:{"WA"}}, ¬
          {folderName:"Se", prefixes:{"SE"}}}
tell application "Finder"
          set theHotFolder to folder "Hal 9000:Users:matthew:Pictures:HotFolderDone"
          set foldericon to folder "Hal 9000:Users:matthew:Pictures:Icons:Rejected Folder Done"
          set fakeTrash to folder "Hal 9000:Users:matthew:FakeTrash"
  ---here
          repeat with matrixItem in fileMatrix -- look for folder
                    set destinationFolder to (folders of desktop whose name starts with folderName of matrixItem)
                    if destinationFolder is not {} then -- found one
                              set destinationFolder to first item of destinationFolder -- only one destination
                              set theFolderName to name of destinationFolder
                              repeat with aPrefix in prefixes of matrixItem -- look for files
                                        set theFiles to (files of theHotFolder whose namestarts with aPrefix) as alias list
                                        if theFiles is not {} then repeat with startFile intheFiles -- move files
                                                  try
  move startFile to destinationFolder
                                                  on error
  activate
                                                            display dialog "File “" & (name ofstartFile) & "” already exists in folder “" & theFolderName & "”. Do you want to replace it?"buttons {"Don't replace", "Replace"} default button 2 with icon 1
                                                            if button returned of result is "Stop"then
                                                                      if (count theLastFolder) is 0 thendelete theLastFolder
                                                                      return
                                                            else if button returned of result is"Replace" then
                                                                      set fileName to get name ofstartFile
                                                                      if exists file fileName indestinationFolder then ¬
                                                                                try
  --next line moves existing file to the faketrash
  move file fileName of destinationFolder to fakeTrash
  move file startFile to destinationFolder
  --if it already exists in fake trash give it a new name then move that file to fake trash
                                                                                on error errmess numbererrnum -- oops (should probably check for a specific error number)
                                                                                           log "Error " & errnum& " moving file: " &errmess
                                                                                           set newName to mygetUniqueName(fileName,fakeTrash)
                                                                                           set name of fileNameto "this is a unique name"-- or whatever
                                                                                           set name of fileNameto newName
  --Now move the renamed file to the fake trash
  move file fileName to fakeTrash
  --now move the startfile to destination folder
  move file startFile to destinationFolder
                                                                                end try
                                                            else -- "Don't replace"
                                                                      if not (exists folder "Hal 9000:Users:matthew:Desktop:Rejected Folder Done") then
                                                                                set theLastFolder toduplicate foldericonto desktop
                                                                      else
                                                                                set theLastFolder to folder"Hal 9000:Users:matthew:Desktop:Rejected Folder Done"
                                                                      end if
                                                                      delay 0.5
  move startFile to theLastFolder with replacing
                                                            end if
                                                  end try
                                        end repeat
                              end repeat
                    end if
          end repeat
          try
                    if (count theLastFolder) is 0 then delete theLastFolder
          end try
end tell
to getUniqueName(someFile, someFolder)
     check if someFile exists in someFolder, creating a new unique file name (if needed) by adding a suffix
          parameters -          someFile [mixed]: a source file path
                              someFolder [mixed]: a folder to check
          returns [list]:          a unique file name and extension
          set {counter, suffixes, divider} to {0, "abcdefghijklmnopqrstuvwxyz", "_"}
          set someFile to someFile as text -- System Events will use both Finder and POSIX text
          tell application "System Events" to tell disk item someFile to set{theName, theExtension} to {name, name extension}
          if theExtension is not "" then set theExtension to "." & theExtension
          set theName to text 1 thru -((length of theExtension) + 1) of theName -- just the name part
          set newName to theName & theExtension
          tell application "System Events" to tell (get name of files of folder(someFolder as text))
                    repeat while it contains newName
                              set counter to counter + 1 -- hopefully there aren't more than 26 duplicates (numbers are easier)
                              set newName to theName & divider & (item counter ofsuffixes) & theExtension
                    end repeat
          end tell
          return newName
end getUniqueName

Answer 1

There are numerous errors in your script, and it's a large script so there might be more, but these are the standouts for me:
At line 48 you:
                                                                      set fileName to get name of startFile
which is fair enough - you then use this to see if the file already exists in the destinationFolder. However, if it does the logic about how to deal with that is flawed.
At line 56 you catch the error:
                                                                                on error errmess number errnum -- oops (should probably check for a specific error number)
                                                                                          log "Error " & errnum & " moving file: " & errmess
                                                                                          set newName to my getUniqueName(fileName, fakeTrash)
                                                                                          set name of fileName to "this is a unique name" -- or whatever
                                                                                          set name of fileName to newName
  --Now move the renamed file to the fake trash
  move file fileName to fakeTrash
  --now move the startfile to destination folder
  move file startFile to destinationFolder
                                                                                end try
so let's focus on that.
56: catch the error
57: log the error
58: generate a new unique filename
59: change the name of fileName to some other string
Hang on, wait a minute.... we already ascertained that at line 48 you defined fileName as a string object that indicates the name of the file. This is just a string. It's no longer associated with the original file... it's just a list of characters. Consequently you cannot set the 'name' of a string, hence your script is doomed to fail.
Instead, what I think you want to do is set the name of the startFile to the unique string. Files have filenames, and therefore you can set the name.
You have a similar problem on line 64 where you try to 'move file filename to fakeTrash'. fileName is just a string of characters. It isn't enough to identify a file - let's say the file name is 'some.psd'. You're asking AppleScript to move file some.psd to the trash. The question is which some.psd? The one on the desktop? in your home directory? maybe on the root of the volume? or maybe it should search your drive to find any/all files with that name? nope. None of the above. You can't just reference a file by name without identifying where that file is. So you probably want to 'move file fileName of destinationFolder...'
There may be other problems, but they're likely to be related - all issues with object classes (e.g. files vs. strings), or not being specific about which object you want.
As I said before, though, I might be way off - you don't say where the error is triggered to make it easy to narrow down the problem. Usually AppleScript will highlight the line that triggered an error. Knowing what that line is would help a lot.