Code:
find $i -type f -name '*.txt' -exec mv {} {}OLD \;
If there is a large number of files, consider using the -xargs option instead of -exec
Or the long way, which gives you a chance to check that you have the right list.
Code:
find . -name DOC* | while read i
do
find $i -type f -name '*.txt' >list
done
OLD=OLD
while read $i
do
mv $i $i$OLD
done <list