I wouldn't put it that way. Some of the songs mentioned have melodic similarities, but they're not "songs with multiple names". "Got My Mojo Workin'" and "High Heeled Sneakers" have melodic similarities, but if you take the original melodies and compare them side by side, they're not the same. Blue Mitchell creating a hip new variation the HHS melody is another thing altogether. The number of variations is endless of course, unless somebody is trying to play a melody as written (in the case of an instrumental version, purposefully retaining the melodic inflections of the original vocal line, for example).
I'm being picky perhaps, but as a musician, I'm slightly uncomfortable with the premise that some of these songs are melodically "the same". That's a bit simplistic, imo.
Thanks for the thought full response, I'd add that sometime the melody line isn't what's defining of 'the song', it could be the groove or the riff or any number of things...