I am pasting this here for my own reference!
for i in `ls files-to-copy-*`; do cp $i `echo $i | sed "s/rename-from/rename-to/g"`; done
What this does is takes each file that is returned of the result of your ls command and pipes it do sed.
This sed command then looks for the part you want to rename and does it (“s/rename-from/rename-to/g” is a regular expression).