For any security issue, you need to figure out what the risk is.
Renaming the file and moving it to an inappropriate directory will stop casual examination by somebody who isn't computer-savvy.
Deleting the file will stop anybody from looking at it without easily available special tools, and will make it time-consuming for them to find it.
Overwriting the file will probably leave nothing findable through the operating system, but that won't guarantee it. If you've processed the file, there might be a partial or complete copy in swap space or equivalent on the drive, and I'm not quite sure what to do about that. Still, failing that, it's probably secure against a reasonable forensic search.
Disk drives no longer present a raw view to the computer using them, though, and it's always possible that the disk wrote part or all of the file on a chunk that it later decided was bad. In that case, removing the disk controller and substituting something more primitive might find a piece of the file. This is getting into very pricey data recovery.
Finally, it's always possible that somebody will be able to read overwritten disk sectors, with some amount of reliability, at some point in the future.
If you're just protecting the mainstream porn from the occasional visiting girlfriend, hiding it in the file system will probably work just fine. If you're terrified that the NSA might possibly be able to read it within the next twenty years, destroy the disk (some of the more paranoid types on Slashdot report fun results with thermite). For most purposes, overwriting the file a couple of times (including at least one 0 and one 1) will do very nicely.