‘Dick’ Cheney ?
Super Dave Osborne
I’m not sure that these, of “Stalin”, really count; these are names these figures crafted for themselves.
Also, I doubt the Dalai Lama or the Thai King’s titles count, either. They are titles that more or less come with the position.
Similarly, mere nicknames which are not descriptive are not what I’m thinking of.
I think to count the name has to be:
(a) descriptive of some quality of the particular person; and
(b) given to that person by other people - not a self-chosen title.
So, “Mahatma” Gandhi counts (and so far, he’s the leader of the pack), Kemal “Atatürk”, and Ludwig “the Mad”.
Gandhi’s the guy to beat. Any later than him?
I see what you did there.
Reagan was often called “The Great Communicator” but he was not primarily known by that name.
Of the examples given in the OP, were those names used by their contemporaries, or are they historical titles? (Also Alexander the Great, etc.)
Not sure if it was an epithet or just a nickname, but Marshal Josip Broz of Yugoslavia was known primarily as Tito.
How about Saparmurat “Turkmenbashi” Niyazov? He died only a couple years ago. Even more recent, Kim Jong-Il is known throughout North Korea as “Dear Leader” (and more recently, as “Great Leader”, a title formerly held only by his father).
If you’re looking for epithets of the form “X the Y”, you’ll probably have to go back at least a hundred years.
For someone still holding office, the Governator.
It was just a nickname (of uncertain origin). Not an honorific.
Tricky Dick
Peanut
The Gipper
Poppy
Slick Willie
Dubya or Shrub
Dalai Lama is just a title; it’s like saying “the Pope” or “the Queen”.
The Decider
It’s a title, like “Pope” or “Patriarch of Constantinople” or “Chief Rabbi of Jerusalem”
Besides, according to Tibetan Buddhism, the same guy has held the title through a bunch of lifetimes.
Though how likely was it that the epithets attached to those ancient statesmen did in fact originate with the statesmen themselves ?
Fidel Castro has been El Lider to Cubans, along with a handful of other sobriquets.
How about the Duvaliers, Papa Doc and Baby Doc?
Well I suppose that Ivan may have wanted to be known as “the Terrible”, but I doubt that Ludwig really wanted to be known as “the Mad”. 
Though one never knows. 
If the [Wikipedia](of the Ivan the Terrible - Wikipedia)explanation is to be beleived then he may well have done:
Gandhis opponent (and fellow Barrister) Muhammad Ali Jinnah who founded Pakistan is usually known as Quaid-e-Azam, the “Great Leader”, or the “Best Leader”. Translations difficult.
I think Queen Elizabeth’s husband is often referred to as Philip the Greek. But I guess he’s not in any actual political position, any more than the first wife is.
He is a prince of Greece and Denmark, though I don’t know if those are meaningful in any way politically.
Not in the running for most recent, but Vlad the Impaler should be mentioned for completeness sake.