At the second congress of the Communist International in 1920 (really its first real congress as the prior was a haphazard meeting of whoever was around at the time) Zinoviev and Lenin presented a series of 21 conditions for left socialists who had split with the Second International for admission to the Comintern. Condition 17 was a standardization of names for parties:

In this connection all those parties that wish to belong to the Communist International must change their names. Every party that wishes to belong to the Communist International must bear the name Communist Party of this or that country (Section of the Communist International). The question of the name is not formal, but a highly political question of great importance. The Communist International has declared war on the whole bourgeois world and on all yellow social-democratic parties. The difference between the communist parties and the old official 'social-democratic' or 'socialist' parties that have betrayed the banner of the working class must be clear to every simple toiler.

So by the end of the 1920 Congress there was a global standardization and centralization of names for Communist Parties—most people in anglophone countries would have been familiar with calling it the Communist Party of (China, Great Britain, USA, India, etc.) already. There was no equivalent for the GMD.