In the case of the Holocaust, this was not always so but rather a development over time. While the term had been around before WWII and had been used to refer to among other things the Armenian genocide, the genocide against the Jews was known until the mid-60s most commonly under the term the Germans used "the final solution" or as the destruction of the European Jews (in his first edition of the standard work "The destruction of the European Jews" from the 60s Raul Hilberg doesn't use the term Holocaust).

The term Holocaust as applied to the killing of the European Jews and Roma and Sinti was only first used in the 60s (Nora Levin's book The Holocaust: The Destruction of European Jewry, 1933-1945 is one of the first examples). It was widely popularized by the 70s when the TV-series "Holocaust" starring among others Meryll Streep premiered on TV and was watched by thousands of people around the globe.

Similarly, the term Holodomor was one first used in the 70s by Ukrainian exile organizations in the US and Canada, partly because they felt in order to spread knowledge of this crime, it deserved a name. But in this case too, it took some time for the general public to associate the name with the crime.

This should answer the question to a certain extent: For some crimes, we use different names because very often victim groups push a certain diction in public in order to gain acknowledgment for the crimes committed against them and to anchor them in public memory and spread knowledge about it. We lack this for example in the case of the Great Leap Forward because either no such effort has been made yet or there are no victim groups in the Western world pushing for it. In case of the Armenian genocide for example, various Armenian organizations refer to it as the Medz Yeghern (the great crime) but that diction has not made it into official language yet - though some historians use it -, partly because knowledge about it is still limited in the public, partly because for official politics, there is still contention about using it because of a state's relation to Turkey.