If it's only something you need for a couple of files every so often, the quickest way is to push F2 on the first file, Ctrl-C, then F2 on the second file and Ctrl-V.
If you need to do it with batches of files then there are a few ways to do that. The best will depend on exactly what you want to do. As a simple, built-in method for batch copying filenames between files, the Rename dialog has a Clipboard menu at the bottom for that. There are also a few scripts for handling specific situations without opening the dialog.