Was shown

[output]

Are the following sentences correct and natural?

My name was shown on the white board. I passed the public exam successfully.

 

[Skrej]

They're grammatical, and natural enough taken individually. Taken together, there isn't an immediate connection between the two without more context.

I'm guessing there's a list of names posted of people who successfully completed a public exam of some kind, and that they only post the names of passers?

 

[Tarheel]

My name was shown on the white board. I passed the public exam successfully.

Two things. One, you don't need "shown". Two, you don't need "successfully".

 

[5jj]

Two things. One, you don't need "shown". Two, you don't need "successfully".

Such obvious points that I missed them completely.

 

[output]

Yes. I have taken a public exam that I passed the exam and my name was shown on the white board. Do you think these expression is natural and making sense?

 

[emsr2d2]

Yes. I have taken a public exam that I passed [strike]the exam[/strike] and my name was shown on the white board. Do you think these [STRIKE]expression[/STRIKE] sentences [STRIKE]is[/STRIKE] are natural and [STRIKE]making[/STRIKE] make sense?

They're understandable but overly wordy. As you've already been told, there's no reason for more than "My name was on the whiteboard. I passed the public exam".