[InJen]

In public examinations, we students do not know the name of one another,

When a group discussion goes on, how can we call one another in English?

[susan53]

I presume you mean if you want to refer to each other, saying something like "I don't completely agree with what XXX said." it would be impolite to use he/she before using the name. So I suggest you ask :
A : I don't completely agree with what.... I'm sorry I don't know your name?
B : Carlo
A: ... with what Carlo said.

Remeber that in examinations (I'm thinking of those like PET, FCE etc) you are marked on the naturalness of your speech and interaction with each other. So being able to do this fluently would be a point in your favour. You'd get a much lower mark if you just "monologued" on the topic when you were supposed to be interacting in discussion.

[InJen]

thank you very much.

I asked this because such a problem never exists in Chinese. In a Chinese discussion, we unexceptionally address othes as "classmate number one, two etc. Does this exist in English?

[susan53]

No. English avoids the use of any sort of descriptive title other than "Doctor" (for medical doctors), "Officer" (for police officers - or their rank might be used : Sergeant, Inspector etc), rank titles for military personnel eg Major, Colonel, and "Professor" (for heads of University departments).

If in a culture it was inappropriate to ask for/use names, then you could use "classmate" "I don't completely agree with what my classmate said...". In International contexts that would sound OK, even though a native speaker would be much more likely to ask for and use the name. But certainly not by number, which would sound impolite.

[InJen]

I also think that will be impolite. It is a cultural difference. Your explanation is very helpful. Thank you very much indeed.