Can I rename OFP mission and addon files?

First of all, if you're talking about officially supplied files installed by OFP, the answer is no. This will negatively affect future upgrade or uninstall procedures.

Further, regarding addons, whether official or unofficial, you cannot rename the addon files because the external file name is what's referenced internally by OFP. If you'll rename  addon files, OFP will still search for the original PBO file name and will not find it.

Regarding unofficial missions, go right ahead and rename the files to whatever you want, keeping the PBO suffix and island name (ABEL, EDEN, etc.) intact, of course. If a mission has a name defined internally, that name is what will always be displayed in the mission list book on the screen. If a mission was not defined a name internally, then the external file name is what will be displayed instead.