Modifying your first script a tiny bit:

<!-- language: lang-bash -->

 #!/bin/bash
 
 for file in ~/Test/Files/*.xfr
 do
 if [ ! -e "$file" ]; then
 echo 'no files were renamed'
 break
 fi
 
 mv "$file" "${file%.xfr}"
 echo "$file has been renamed" 
 done > ~/Test/log.txt

I've done two things here:

1. The redirection to the log file would truncate the log file in each iteration, so I've moved it to the end of `done` instead so that it redirects all standard output of the loop.

2. If the pattern does not match any filenames, it will remain unexpanded by default. I detect this with a `-e` test and output a special message. Then I `break` out of the loop.


Alternative:

<!-- language: lang-bash -->

 #!/bin/bash
 
 for file in "$HOME/Test/Files"/*.xfr
 do
 if [ -e "$file" ]; then
 mv "$file" "${file%.xfr}"
 printf '%s has been renamed\n' "$file"
 else
 echo 'no files were renamed'
 fi 
 done >"$HOME/Test/log.txt"

Here I've just changed the flow a bit and used `$HOME` in place of tilde (looks nicer in a script IMHO). I'm also using `printf` instead of `echo` as it's generally safer for outputting variable data (see e.g. "https://unix.stackexchange.com/questions/65803").


Both alternatives above may also run with `/bin/sh` rather than `/bin/bash`.


Another alternative, if you want to write more of a "report":

<!-- language: lang-bash -->

 #!/bin/bash
 
 shopt -s nullglob
 
 xfr_files=( "$HOME/Test/Files"/*.xfr )
 
 for file in "${xfr_files[@]}"; do
 mv "$file" "${file%.xfr}"
 done
 
 printf '%d files renamed\n' "${#xfr_files[@]}"
 if [ "${#xfr_files[@]}" -gt 0 ]; then
 printf '\t%s\n' "${xfr_files[@]}"
 fi

This sets the `nullglob` shell option in `bash` which makes patterns expand to nothing if there are no matches. It then writes out the number of files renamed and if this number is greater than zero, it also lists the filenames with a tab indent.


---

In your updated question, you use the variable `PATH`. This happens to be the variable that holds the search path for shell utilities, and setting it to anything other than a `:`-delimited list of directories will likely make the shell unable to find `mv` and other common tools.

In general, avoid using uppercase variable names in shell scripts, and instead use lowercase or possibly mixed-case variables. This way, you avoid accidentally overriding important variables that the shell may use.