Different given names in Chinese and English
There's no system; English names can be chosen essentially randomly, and the reasoning (if any) behind the choice may not be obvious unless the person explicitly tells the backstory behind the name.


Ma Huateng's (馬化騰) name Pony comes from the Chinese practice of adding the prefix 小 in front of the family name to indicate informality or affection for young people as the addressee, which becomes 小馬 (Xiǎo Mǎ), as 馬 (Mǎ) is his last name. 小馬, as a Chinese word, literally means Pony.
Zhang Zhidong's (張志東) name Tony doesn't seem to be explicitly explained, although one can infer that it might have been chosen for one or more of the following reasons:


Tony sounds similar to 東 (Dōng), the last character of his first name;
Tony was chosen to rhyme with Pony.

Jackie Chan's name came about because he worked under a construction worker named Jack; he was known as Little Jack due to his apprentice role, which later changed to Jackie.