I too once suggested changing the names of the .exe files, but it turns out that requires too many other changes; so I think now we're only talking about changing the names of the .7z files on @roytam1's page, some default prefs (so various links would point to Web pages controlled by @roytam1 vs. MCP), the displayed names, and the logos. The .exe file names would remain the same, and the other changes shouldn't affect add-on compatibility.
It is a lot of work in total, though - as @Sampei.Nihira noted, there are several Help menu links to fix as well - and the work is probably best suited to a Web designer, which I am not. I've already suggested names (Titan; Apophis) and could probably even create logos, but not all the necessary Web pages based around them - at least not if you want them to look decent!
The benefit to be gained depends on how likely Matt or MCP is to take drastic action (such as making PM/Basilisk closed-source, thus cutting us off from all future enhancements) next time they think @roytam1 is to blame for unwelcome New Moon/Serpent support requests. Rebranding won't end those unwelcome requests, but it would give @roytam1 a good defense against their likely future complaints.