I refuse to believe that there would be a planet whose full name is "Alpha III." That's just silly. It would have to be Alpha Something III. Unless it's a reference to a space station or something rather than a planet in another star system.
Yeah, it is kinda silly. Unfortunately, TOS did this a fair bit: Beta III, Omega IV, Omicron IV. And TMP gave us Delta IV. So, the original episode writer did probably intend for it to be a planet whose full name is Alpha III.
, impressive list. I don't have much to add, but since you mention Deneva's destruction in its entry, just thought I'd mention that