How about this? I am supposing that the target directory is in the file new_dir.txt.
#!/bin/bash
new_dir=$(cat new_dir.txt)
now=$(date +"%Y%m%d%M%S")
if [ ! -d $new_dir ]; then
echo "$new_dir doesn't exist" >&2
exit 1
fi
ls | while read ls_entry
do
if [ ! -f $ls_entry ]; then
continue
fi
if [ -f $new_dir/$ls_entry ]; then
cp $ls_entry $new_dir/$ls_entry\_$now
else
cp $ls_entry $new_dir/$ls_entry
fi
done