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In addition to StrongBad's answer, this kind of behavior would also discourage students from asking questions in fear of finding themselves on the “stupid questions and answers” list. Given that “unacceptable” wasn’t defined further in the original question, I think this is also an important aspect that makes this sort of student shaming unacceptable. Except if the Professor doesn’t actually want any questions asked of course :-)

I'd like to add that additionally, I don't think posting photos of test answers online (like this specific professor did) is ethical or even legal. According to this website (archive link), handwriting is personal data according to the EUs GDPR (General Data Protection Regulation) and can almost certainly not be published without permission.

It's not only that such ridiculing is absolutely unacceptable and counterproductive (as others mentioned already) but it also puts the academic themselves in a kind of bad light as a lecturer/teacher. If my third year math/engineering students didn't know what the cotangent is I would consider it much more of my own fault rather than theirs.

And most importantly, one shouldn't be embarrassed of not knowing something but of not wanting to get to know it. Most people don't even bother to ask a question even being proud of their ignorance sometimes. So I believe that no curiosity should be frowned upon.

UPDATE: Having said the above, it could still be considered a good attitude for a student to come up with some answer themselves (i.e. do some research/thinking) prior to asking their professor a question.

This is a bad taste, for sure (IMHO), but since there are plenty of websites where students are more than welcome to tell anything they want about their professors with full names etc., I guess this may be viewed as a kind of "symmetric response". I'm pretty much against internet trashing of anybody (usually it does more bad than good for all parties involved) but, alas, it has became a pretty common culture nowadays, so I am not surprised that some professors resort to it too.

As to the questions listed, they do not show stupidity, just utter ignorance, so I personally would object more to calling them "stupid questions" than to listing the student names. If a third year student asks me what a geometric progression is, I just answer with a definition and an example and consider the case closed. Moreover, I can openly announce that at the moment of this writing I don't remember what exactly a decibel is myself. All I remember is that it is a unit of measure of sound intensity and that the scale is logarithmic. If the student is not able to process an answer appropriately, it is, of course, a completely different story, but if one just doesn't know something, there is no shame in asking.

This means that I would neither call such questions stupid, nor list the names myself and would, probably, discourage my friends from doing so, but I wouldn't cry out loud "Unforgivable crime!" or "Unethical behavior!" if I see somebody else doing it either. For me it is bad taste, period.

That was the "common sense" part. As to the legal part, it is country dependent and I'm not really familiar enough with the European laws to discuss the corresponding subtleties.

Not only the ethic behind this is very doubtful as StrongBad said, but this is also probably illegal under the loi informatique et liberté & the GDPR because it falls under the definition of "Donnée Personnelle" (see the CNIL definition). If someone decide to warn the CNIL about this page, it could put the university and the teacher at risk.

As has been said in prior answers, it is NEVER acceptable to make fun of students or otherwise say or do something that could prevent them from learning.

Many sites on the Stack Exchange network would not be the same without “stupid questions” and you could view students asking them in the same way. Even if it seems utterly ridiculous to you, the student likely is honestly wondering about it and laughing at their questions somewhere where they could potentially see them could encourage them to not ask questions for fear of being laughed at. Students who hold their questions for this reason often never get them answered and as a result earn a lower grade.

1) First of all, it seems that the leading question of the discussion "Is it acceptable to publish student names with the label stupid question?" is not correctly formulated. A part of the the question contains a statement which is actually faulty: the names of the students are not revealed, only the first names are mentioned, which are all very common ones. The format like Donald T. or Emmanuel M. does not permit to identify the person, so that the anonymity is fully kept (hence, GDPR has nothing to do with this). Moreover, such a format of names is usual in classic literature. Actually, to name the person only with her/his first name means precisely that you do not want to reveal the identity of the person.

2) I don't think that the objective was to ridicule the students, but rather to make them attend more or/and to make them understand that they are simply too lazy (since they do not recall even basic notions). In engineering schools, as was remarked earlier by @A Simple Algorithm, students should have at least basic notions of the trigonometry (the trigonometry is usually covered in high school before the university), because it is used throughout all the university curriculum. Same remark concerns decibels: this is a very basic notion, which is covered during the 1st year of studies. So (@J.R.) nobody mocks. After all, it ain’t funny to have students with such a poor level.

3) In France, the higher education is free, so that it is easily accessible even for the lazy students. Don't you think about those students from other countries, who have a talent and would like to study, but can't do this because their parents can't pay??

4) Also, I don’t understand why it is acceptable to widely rank teachers and professors on the Web sites, and why it is not acceptable to do the same with the students (thought on this Web site the rank of the students is not published)? And on the Web sites, the professors are fully named, not as Antoine W. or Sven F. So strangely, nobody thinks about GDPR or FERPA for the professors and teachers.

UPD: the initial question was modified so that now it is clear that the actual names are not revealed on the website in question.