How did the students figure this out?

Question

A Logician meets with five of his new students. These students have never met before and do not know each other's names. The logician goes to the board and writes all their names in random order.

SAL SMITH

TAYLOR LI

ROSA WILSON

ALEX JONES

ALI NA

He says:

I know you do not know each other's names. Here is what I want you to do. Any one of you can write down the following statement on the board:
My name is not ______
The blank must be a first name or a last name and must be a single word. After seeing that, are the others able to guess that person's name? AND can that one sentence lead you to correctly guess all the other student’s names? No talking to each other of course.

The students thought about it. They realized the following:

1. Four of the five students were girls and one was a boy.

2. Four of the five first names were gender neutral. One (Rosa) was not.

3. Two of the five students were Asian (Chinese)

So here is what happened.

A student wrote on the board: MY NAME IS NOT _______

Immediately all the others knew who that person was.

Then, two other students came forward and said: I know each and every student’s names. Then those students proceeded to correctly identify all the names.

Who was the first student and what name did he/she write in his/her written sentence?

How did everyone else identify him/her?

Which were the other students who correctly identified everybody?

How?

Answer 1

Here is one way this could have happened.

The two Asian students are both girls. One of them steps forward and writes "My name is not Taylor/Ali", writing the Asian name that is not their own.
Everyone can now obviously identify the two Asian students because there are only two Asian names and it is now clear which way around they go.
Of the three non-Asian students, the girl who is not Rosa can figure out the remaining names, because obviously the boy is not Rosa so must be Sal/Alex (whichever is not the girl's own name).
As soon as the girl steps forward, the boy also steps forward. He made the deductions above too, so knows that the girl who just stepped forward is not Rosa, so must be Sal/Alex (whichever is not the boy's own name).
So Sal and Alex stepped forward and are able to determine everybody's names. Rosa and the two Asian girls are not able to distinguish between Sal and Alex.