Who was the last leader of a country to call himself a dictator, or the last regime that called itself a dictatorship?

I would assume Caesar.

Rome was, I believe, the last state that had this as an official title, so he would've called himself a dictator.

It used to be a title for a limited amount of time. The citizens would elect one to meet a crisis. He did want to become dictator for life, but as we know, this wasn't met with general approval, and specific action was taken to end his life (and dictatorship).

Douglas MacArthur as Supreme Commander of Allied Powers in Japan after WWII. President Truman gave him absolute power over Japan.

He might be described as a shogun (military dictator). Actually, according to wikipedia, "The Japanese subsequently gave MacArthur the nickname Gaijin Shogun ('The foreign Shogun') but not until around the time of his death in 1964".

In fact, he was a dictator in the roman way. Called to serve for the country and retire after completed the job.

I'd like to put forth another example of a country's current leader calling himself a dictator or rather his (plans for the) country a dictatorship:

During an official visit to Vienna in 2014, Vladimir Putin was asked what his plans for Russia looked like. He smiled and answered in German:

Diktatur.

then he (seemingly) hastily injected:

Aber gute Diktatur.

(Dictatorship. … But good dictatorship.)

Vladimir Putin is known to be 'fluent' in German. On one hand, fluent (without apostrophes) may be a bit exaggerated, as high ranking people typically get more credit than actually deserved. On the other hand, according to his German Wikipedia article, he served as interpreter for Boris Jelzin in meetings with Helmut Kohl.
However his injection leaves little doubt that he knew what he was saying and how people could take it.

At the time, it was commented as him joking about his strong man image. I don't quite recall, if it was also around his official speech in German parliament (Bundestag) in 2001 or during consultations with German company leaders. He might have pulled that 'joke' multiple times.

I remember quite vividly that I saw video clips of both occasions in a documentary about Putin that analyzed his reign.

@José Carlos Santos mentioned a period of military dictatorship, which is probably the most correct answer.

Nonetheless, the Dictatorship of Garibaldi (Italy), also answers your question, as he did call himself a dictator, as seen in the Decreto col quale il Generale Garibaldi assume la Dittatura in Sicilia

It should also be noted that those answers that mention the concept of dictatorship of the proletariat are erroneous if you want dictatorship as a political system. In Marxism, it is termed dictatorship because the state apparatus, as an instrument of class oppression, is used to exercise control by a social class over other social class(es). Thus, the existence of the opposite dictatorship of the bourgeoisie. As such, the term denotes a type of state of affairs in society, and not a political system. Hence, according to its proponents, the existence of, for example, the term democratic dictatorship of the proletariat, where democratic is used to refer to the political system, and dictatorship of the proletariat to the state of affairs.

This may be not exactly an answer, but it may be useful. I have come upon a case of a leader's use of “Dictator” in 1898, later than Garibaldi, and as an official title, rather than a more informal self-description as has been shown of Presidents Lukashenko and Bukele of modern Belarus and El Salvador: Dictator Emilio Aguinaldo of the Philippines (Wikipedia). Wikipedia cites the National Historical Commission of the Philippines, which says that:

• Aguinaldo led a “dictatorial government” from 24 May 1898, using the title “Dictator” until he changed it to “President” on 23 June 1898;
• “By July 1898, the Filipinos liberated the provinces of Cavite, Laguna, Batangas, Pampanga, most of Bulacan and the suburbs surrounding Manila”.^[1]

The first four provinces — Cavite, Laguna, Batangas, and Pampanga — have, within their modern borders (as of 2007),^[2] a total of 867 424 hectares, or 8674.24 km², more than 3.35 times the 2586 km² of Luxembourg.^[3]

However, with Aguinaldo's time as "Dictator" lasting from 24 May to 23 June, he fell one day short just over 50% short of the two-month minimum, and he didn't spend all of that time in control of all four of those provinces. On the other hand, if it is acceptable that the leader call himself a dictator at one time and control a Luxembourg-sized area for two months at a different time, then Aguinaldo may qualify still.

Someone familiar with Philippine history (which I am not) may be able to provide more detail (and maybe better sources than an understandably patriotic Web page of the Philippine government).

References

• [1] "The First Philippine Republic", 7 September 2012, National Historical Commission of the Philippines, https://web.archive.org/web/20211007035227/https://nhcp.gov.ph/the-first-philippine-republic/
• [2] "List of Provinces", 31 March 2016, Philippine Standard Geographic Code Interactive, Philippine Statistics Authority, https://web.archive.org/web/20160419000512/http://www.nscb.gov.ph/activestats/psgc/listprov.asp
• [3] "Luxembourg", 28 December 2021, The World Factbook, U.S. Central Intelligence Agency, https://web.archive.org/web/20220112011745/https://www.cia.gov/the-world-factbook/countries/luxembourg/

Marxists have been using the term dictatorship of the proletariat in the positive sense long after the word become an grave insult for Western liberals. In the USSR, it was not until 1934 when XVII Congress of CPSU proclaimed that the socialism has won and the need for dictatorship of the proletariat is over. But it still was mentioned (as a matter of history, but still positively) in the USSR Constitutions of 1936 and 1977 and in the Party documents. Of course it did not mean in any way that the rule became less dictatorial - it was just the apparent change of rhetoric of the ruling party in the USSR in the 1930s.

In other countries, as shown in LangLangC's answer, the communists may keep the traditional rhetoric.

Note that ideologically (and in sharp contrast with the practice) Marxists were never fond of personal dictatorship, they always pointed out the difference between the good dictatorship of the proletariat and the evil dictatorships in the capitalist countries, and of course did not tolerate when anyone called their leaders for dictators.

The Centrocaspian Dictatorship ruled from July to September 1918 in and around the city of Baku in current Azerbaijan. This anti-Soviet country was not recognised by any other and soon overrun/replaced by the Azerbaijan People's Republic. As far as I know, no more recent state (recognised or unrecognised) had the word dictatorship in the name of the country.

Alexander Lukashenko has been the president of Belarus since 1994. He called himself "the last and only dictator in Europe" in a 2012 interview.

Q: Some Western politicians call you a dictator. What is your reaction?

A: I ask myself what is a dictator? I don’t understand. It is some kind of terrible person, a bad person. But I am not frightening, I am not a bad person at all. ... I am the last and only dictator in Europe and indeed there are none anywhere else in the world.

However, I think the government of Belarus does not formally refer to itself as a dictatorship despite its autocratic behavior.

Since 2019 the El Salvadorian President Nayib Armando Bukele Ortez is in office.

The current developments were characterised as

"precursor to a dictatorship," and a representative from the FMLN stating that the state is serving only one person, referring to Bukele. […]

Despite being described as an autocrat and an authoritarian, and despite self-proclaiming himself as the "Dictator of El Salvador," the "coolest dictator in the world," and the "Emperor of El Salvador," Bukele has retained a high approval rating throughout his presidency.

Some might say that he used this style "ironically". Fact remains: he called himself that way.

"Was" is the wrong tense used here.

The basic task of the nation in the years to come is to concentrate its effort on socialist modernization. Under the leadership of the Communist Party of China and the guidance of Marxism-Leninism and Mao Zedong Thought, the Chinese people of all nationalities will continue to adhere to the people's democratic dictatorship and…

— Constitution of The People's Republic of China — Preamble

My guesses here not to be proven by linked evidence include: that China is roughly a bit larger than Luxembourg, the "at least two months in power" criterion is fulfilled for the ruling party there.

This is not over, and you will be happy.