Based on what I've learned about the Chinese Communist Revolution, the Communist Regime did not try to distance themselves from Sun Yat-Sen. However, Sun Yat-Sen supported a Western-style representative republic. From my viewpoint, as an American, it seems as if the Communists pretty blatantly hijacked and destroyed any hopes of fulfilling Sun's revolution.
Yet, the Chinese still honor Sun and seem to view modern China as what he would have wanted. How did a one-party dictatorship convince the people of China that their government was somehow honoring Sun's goals?
To say 'Sun Yat-Sen supported a Western-style representative republic' oversimplifies Sun's views on revolution, republicanism, and nationalism. For one, the idea that a stable enlightened democracy would spontaneously emerge from the ashes of imperial China is naive. And furthermore it didn't. The first revolution in 1911 (the Xinhai Revolution) was hijacked by the powerful general Yuan Shikai, to whom Sun ceded the title of provisional president in exchange for forcing the last Qing emperor to abdicate. And because of his military power, Yuan was able to sideline Sun and his party (the GMD) as well as oversee the erosion of the first Republic of China and finally a reversion back to monarchism with himself as Emperor. After Yuan's death in 1916, China was plunged into a era of regional warlords.
Nationalism lay at the core of Sun's political philosophy and he was concerned with fundamentally reforming China and its people - not merely carrying out token democratic reforms in a backwards nation. In Sun's Three Principles of the People, the principle of Nationalism makes an appearance before the principle of Democracy (Nationalism, Democracy, Livelihood). From his A Program for National Reconstruction (1918) we can see as to why he thought this:
It is not to be denied that the Chinese people are deficient in knowledge. Moreover, they have been soaked in the poison of absolute monarchy for several thousand years [...] the Chinese people, being for the first time under republican rule, must have a farsighted revolutionary government for their training. This calls for the period of political tutelage, which is a necessary transitional stage from monarchy to republicanism. Without this, disorder will be unavoidable.
The key word here is "political tutelage", which is to be administered by a "revolutionary government"; in essence, the people must be prepared for democracy or they won't be ready for it. A revolutionary government isn't an elected constitutional government because that would be putting the cart before the horse. Instead, the existence of an authoritative revolutionary government arises from a military revolution to first consolidate power. This is evident from Sun's division of National Reconstruction into three phases: 1. Destruction, 2. Transition, and 3. Reconstruction. Destruction here isn't a mere metaphor, but an "extraordinary" and violent phase to overthrow the existing establishment and oversee the elimination of archaic customs, etc. After a period of successful destruction, the transitional phase begins:
... the provisional constitution will be promulgated in the district, defining the rights and duties of citizens and the governing powers of the revolutionary government. [...] When the constitution is promulgated and the president and the National Assembly are elected, the revolutionary government will hand over its governing power to the president, and the period of political tutelage will come to an end.
In 1918, Sun is overly optimistic by suggesting that a period of 6 years would be sufficient for such a transition. In later writings he will avoid giving any arbitrary time-line. Naturally, the length and exact nature of this transitional phase will be open to interpretation, debate, and much controversy.
This now brings us to the statement 'the Communists pretty blatantly hijacked and destroyed any hopes of fulfilling Sun's revolution'. Setting aside Yuan Shikai's usurpation, this statement skips over the twenty-four crucial years of modern Chinese history from Sun's death in 1925 to the 1949 establishment of the PRC. After Sun's death, his vision of a national revolutionary movement uniting China was superficially realized by his party's successor Chiang Kai-shek's successful Northern Expedition against the Warlords. Chiang's model of nationalist reform would at least in theory mirror Sun's. Having conquered China, he was now in the transitionary or tutelage phase with himself as head of Sun's former Nationalist party (GMD or KMT) and therefore the leader of a single-party Chinese state. Although frequently referred to as a fascist dictator or generalissimo, Chiang's de facto power was checked by i) warlords whom he allied with during the Northern Expedition who still retained considerable power; ii) his purge and massacre of communists within the GMD leading to the splinter of the Chinese Communist Party (CCP) from the GMD and their subsequent civil war; iii) burgeoning influence and agitation in Manchuria by Imperial Japan followed by a 1931 invasion and eventual war (Second Sino-Japanese War -> Second World War).
It was only in 1947 that a new Chinese constitution was promulgated with Chiang formally elected as President of the Republic of China in 1948. However the years after the end of the Second World War only marked a new phase in China's instability. The civil war had been renewed; the communists had fully taken advantage of the Second World War to ingratiate themselves with the Chinese peasantry and to entrench themselves as a formidable military force. Chiang's political capital as a nationalist leader had been severely drained as a result of the Xian Incident (u/ScipioAsina). Furthermore, marred by widespread government corruption and incompetence corresponding with hyperinflation taking root from the beginning of the Second Sino-Japanese War, Chiang's government had long ceased to be the revolutionary government that Sun had idealized. Within two years of being elected as President, Chiang would escape to Taiwan.
It should now be clear why the CCP holds Sun as a nationalist hero: 1. He was first and foremost a nationalist who helped overthrow dynastic rule; 2. His conception of republicanism is not inconsistent with single-party rule; under the GMD, China was also administered as a single-party state; 3. the CCP sees itself as the legitimate successor to Sun's revolution as opposed to Chiang's led GMD.
"Selections from A Program of National Reconstruction: "The Three Stages of Revolution" (1918)" By Sun Yat-sen, from Sources of Chinese Tradition: From 1600 Through the Twentieth Century, compiled by Wm. Theodore de Bary and Richard Lufrano, 2d ed., vol. 2 (New York: Columbia University Press, 2000), 328-330
"The Inflation in China", Andrew C Huang, The Quarterly Journal of Economics, Vol. 62, No. 4 (Aug., 1948), pp. 562-575