snoe got it.
Is the full set you’re referring to FDR, LBJ, and JFK? Or, are you counting less-used ones like DDE or RMN or other?
As with all historical events or cultural conventions, that’s a safe guess :). But see below
There are only so many kinds of cabin 
Almost!
Not DDE or RMN, certainly. I can think of one “other” example, at least…
Were all their middle names actually older family surnames?
Yup!
Sounds like it might be true, but not the explanation I was looking for. I’m sure that there are some non-shortened presidents for whom that’s true as well (Ronald WILSON Reagan, as a guess).
It’s not at all obvious to me, so I guess I’ll just list them.
Was it HST? GRF? (LLK?) JEC? RWR? GHWB? WJC? GWB? BHO? DJT?
Total length of names?
I’m wondering who “LLK” was, but none of those abbreviations completes the set, either.
Be more specific…
The commonly-abbreviated names have the longest surnames: Kennedy, Roosevelt, and Johnson. It would save less space to simply write “Bush” or “Nixon” since the lower-case letters are smaller. And Eisenhower can be called “Ike”?
LLK was Leslie Lynch King, Jr. of course. Our 38th president.
I’m baffled how the set could not have been completed, so I guess I’ll dig deeper into the question.
By “US Presidents” did you mean persons who had held the office of “President of the United States”?
By WWII did you mean World War Two?
By ‘initials’ do you mean the first letter of each of their names?
Wait, did you mean WJB? That’s even more obscure.
Does the set you are referring to include fictional presidents?
Gosh, I never realized all those eye transplant patients were so suicidal. Doesn’t show up in the obituaries so often.
Well, “Ike” is not “DDE.” Sorry to nitpick :(. I think I answered your original question about DDE accurately … I read it as referring to nicknames, not to the presidents themselves.
ZipperJJ and Ludovic basically got it. The presidents with the most familiarly abbreviated names – FDR, JFK, LBJ, and Ike – all had last names that were seven characters or more in length, and would hence reduce the font size of newspaper headlines.
The other ten presidents all had six-character-or-fewer last names: Truman (6), Nixon (5), Ford (4), Carter (6), Reagan (6), Bush (4), Gore (4) – just kidding! Bush again (4), Obama (5), and Trump (5).
Why didn’t we shorten Bill Clinton’s name, though? He’s got 7 characters in his surname. But one of them’s a skinny old “i” – enough to squeeze into a decent-sized headline!
This may be a bit of a “Just So” story – euphoniousness (who wants to say “RWR” out loud?) and other factors may have contributed as well. Still, the answer was deducible from the question with minimal knowledge, so I thought it was worth throwing out there.
I got this explanation from one of the pieces in Hendrik Hertzberg’s excellent journalistic anthology Politics; I was hoping to quote it, or at least cite the relevant piece, but a) I’ve lent my copy out or lost it and b) the relevant passage is not on Google Books or Amazon’s “look inside” preview. So you’ll just have to buy a cheap, remaindered copy and hunt for it yourself. Hertzberg gives details about point sizes, etc.
Postscript: If a hint was needed, I was going to point out that this “issue” is unlikely to arise with future presidents.
I agree that Ike is not DDE, but I’m baffled as to whose initials you are claiming it is…
So, I guess you were using a very novel definition of the word “initials”. It was my third question that illuminated your deception. Do you have any source which defines the word initials such that a modern president could be referred to in this fashion?
As an aside… I find that it’s difficult to remember General Eisenhower’s first name, but not at all difficult to remember President Eisenhower’s. Not that that makes any sense, of course.
Ah, I see. I was not, I think, dishonest in how I phrased the actual question; see above. The reference to initials was in the table-setting; in the question, I did not specify that these presidents’ names were commonly shortened in this way or something like that.
(I did try to imply it, as previous puzzles implied that a cabin was a small house or home was where someone lived.)
Eisenhower and Clinton were the outliers that made the pattern more complex and tricky. And interesting, I hoped.
Sorry if it seemed unfair, though. 
I thought it was a great question. I’m sure other people here have obscure trivia like this they could contribute.
I guess I’ll go again if no one else minds. This one was new to me from a podcast on lateral thinking. I’m not sure if it is a good one or not. I guess we’ll see.
A man in uniform stands on the beach of a tropical island. He takes out a cigarette, lights it, and begins smoking. He then opens a letter and begins reading it. The cigarette burns down between his fingers, but he doesn’t throw it away. He then cries. Why?