I am looking for the easy way to rename all images, or other groups of multiple files, together in OS X Mavericks.
Is it possible with Preview or any other standard OS X application?
You can use OS X's Automator.app to quickly rename batches of images. The Actions you want are:
Using this approach you can rename files, change the case, or append/remove specific parts of the original file name.
To learn more about using Automator, see Apple's Mac Basics: Automator.