Here are two examples that use while loop.
In the next example, the content of the file called list will be redirected to the while loop, where each line will be read as value of the variable $FILE_NAME, that will be used as an argument in the mv command.
while IFS= read -r FILE_NAME; do mv "$FILE_NAME" "/dest/dir/"; done < /path/to/list
In the next example, the command cat will output the content of the file called list. The output will be piped to the while loop, where each line will be read as value of the variable $FILE_NAME, that will be used as an argument in the mv command.
cat /path/to/list | while IFS= read -r FILE_NAME; do mv "$FILE_NAME" "/dest/dir/"; done
IMO using redirection is the better way. Here is provided more detailed explanation abut this usage of while: While loop only processes the first entry of ssh command.