Design Studio

I don't think there's an easy way to do this. Folders may be the easiest way to organize.

To rename requires you to re-upload the file, which will also BREAK your templates or emails that rely on these files.

You should be able to organize by folder as Kim suggests. I usually do:

Email
-Email Template
-Email X
-Email Y
Whitepapers
Landing Pages
-Template X
-Page 1

The folders do not affect the URL that Marketo provides.

We've recently gone through this exercise.  As Kim and Josh mentioned, you can't rename unless you re-upload so it is best practice to name your files a certain way prior ot uploading.  

In addition to Josh's recommendation, we've also made good use of the "Archive" feature to clean up files we don't want to show up in search but don't necessarily want to delete.

I use folders for images and files.  
I have folders for each department for email templates, landing pages and images:
Events
Marketing
Research

For images and files I break it down whether it's an image or a PDF file and they go into the following folders
By publication, bookstore, events, advertising, sponsorship
Subfolder:
images for promotions
images for renewals
images for conversion series
images for publication fulfillment

PDFs:
By publication name
Advertising
Events

Snippets is broken down by:
Marketing footer
Events footer