I have encountered similar situations where I need to copy and rename files. So I wrote a function to handle many copy and rename configurations. It's a convenient way of copying and renaming large groups of files using lists and wildcards. It's called "easycopy" and is available on the Matlab File Exchange.
(There's also a sister function, "easyrename" which does the same searching and find-replace, but with a move/rename command.)
Here's how it works in the exact situation described by bluegin.
ORIGINAL DIRECTORY: ...copy2\001X.txt, ...002Y.txt, ...003Z.txt
NEW DIRECTORY: ....copy2\newdir
COPYING FILES ...