That's actually what PPVEnabler does. It moves them to that folder. That's why they get uploaded with iPhoto, because iPhoto uploads the DCIM folder.

You'll see a Symblink at /private/var/mobile/media/Videos that takes you to the CycorderVideos folder. Because Cycorder looks for the /media/Videos folder but that is now only a link so they get placed in the DCIM subfolder.
Cycorder does not save videos name that. They are only numbers with no IMG. But no, there is no way to change them.
I looked into this, because if you use iFile and DO rename one of the Cycorder videos to IMG_9999.MOV (Note I used large numbers so there is no conflict with the camera and I made the extension all caps) and put it in the DCIM folder you can access the videos in Camera Roll to edit them or whatever.
Also, Cycorder video files are being named so there will never be a conflict at the moment. Each file name is the Unix time that it was recorded.
http://en.wikipedia.org/wiki/Unix_time