For added security, you can choose to have your filenames scrambled upon upload. This will add a short hash to the end of your filename, making it much more difficult for others to guess the name of your other files.
Or click on your username in the upper right corner of the screen and select User Settings. Under the Privacy tab , you will see two options on the middle of the page regarding the file name scrambling
For Future Uploads:
This option allows you turn on/off the scrambling of your file names for all future uploads. If you enable it (checking the box), all of your file names will be scrambled on upload. If you uncheck that option, any future uploads will keep the same file name, and the scrambling will not occur.
For All Previous Uploads:
If you have uploaded previous images and wish for the file names to be scrambled, you can select this bar, and all previously uploaded media will have their file names scrambled.
If you scramble your filenames for previous uploads, all links in your account will be broken! Your images will no longer display where they are linked out, and there is no way to unscramble the filenames.
If you are worried about the privacy of your images, I would suggest enabling the file name scramble feature.