Thank you for provoking me to resolve the issue on my own. I had to google some things about applescript in order to realize that the order of sytanx in literal to the working order of the script. I now understand what the script does in detail... THANK YOU!
I moved the following line of code:
-- csv contents as list
set csvList to paragraphs of (read csvFile)
The ruslting script is this:
-- choose the folder
set workingFolder to (choose folder "Select the folder to be processed") as text
-- change this to specify the correct csv delimiter
set splitDelimiter to ","
-- change this to specify the file name join character
set recombineDelimiter to "_"
tell application "System Events"
-- choose the csv file automatically: need to specify name extension
set csvFile to (POSIX path of (first file of folder workingFolder whose name extension is "csv"))
-- csv contents as list
set csvList to paragraphs of (read csvFile)
-- list of files in alphabetical order
set fileList to (POSIX path of (files of folder workingFolder whose visible is true and name begins with "untitled"))
repeat with i from 1 to count of fileList
-- get a line from the csv list, split it at the delimiter, and recombine it
set {oldTID, my text item delimiters} to {my text item delimiters, splitDelimiter}
set newFileNamePieces to text items of (itemi of csvList)
set my text item delimiters to recombineDelimiter
set newFileName to newFileNamePieces as text
set my text item delimiters to oldTID
-- get a file from the file list and note its extension
set currentFile to file (itemi of fileList)
set fileExtension to name extension of currentFile
-- write the new name back out to the file
set name of currentFile to (newFileName & "." & fileExtension)
end repeat
end tell