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In English, sometimes we'll refer to a person whose name is unknown or undisclosed as "Person A" particularly in hypothetical scenarios. Does a similar thing exist in Chinese that doesn't make use of English letters?

You would say

甲、乙、丙、丁……

They come from 天干, you could also say

路人甲、路人乙、路人丙……

In the case where you know his or her surname, you could also say

李某、王某……

In case if you want the specify that person's identity

某市民、某员工、某政府工作人员……

To refer to someone non-specific, you can say「某某/某人/某某人」.

我廠「某人」偷了東西，我不點他的名字，他應坦白交代。

Someone in my factory was stealing things. I won't mention him by name, but he should come forth honestly and explain himself.

To refer to Person A or Party A, for example in an agreement or contract, you can say 「甲方」(as opposed to Person/Party B「乙方」or both parties「雙方」).