In this question: My paper was withdrawn from predatory journal after publication, what should I do? the OP is considering naming the publisher and a high rep user has recommended them to do this. I personally do not think naming the publisher adds any value and I do not want AC.SE to be a place to list bad publishers and researchers. If naming the publisher, journal, or researcher adds value to a question or answer, then I think it is important to name names. In cases where naming names is simply to shame publishers/people, I think it is a bad idea.
I think that, while naming people is inappropriate and not constructive (example: grad student complaining about their supervisor Prof. Doe to be a mean, mean person), publishers are another story.
As commercial operations, they accept to be public entities and it's practical to the community to be able to discuss about a specific company (see for example this: Do Springer, IEEE, Elsevier charge a fee for non-open-access journals?), the same way we discuss the pros and cons of, say, a reference manager software. For example, there are several questions about Elsevier's editorial website (example: How can co-authors check the status of a submitted manuscript in Elsevier Editorial System?).
The same holds for universities. Why put universities under scrutiny (What is the status/reputation of the University of South Africa (UNISA)?) but not publishers?
Additionally, if a scholar is wondering about a given publisher, chances are the query will be more along the line of: Is Lambert Academic Publishing a reputable company? or Is MDPI a reputable Academic Publisher? than 'What is the process to evaluate the shadyness of a given publisher'.
There are also multiple comments and answers that are critical about the business model of established publishers and I think it's very well, but we should also be able to openly criticize the smaller, less experienced, and especially the dishonest ones.
I agree that there is no benefit to naming names, and it can be detrimental to do so.
Besides, if a question requires the name of the publisher in order to be answered, it's probably too localized, anyways (as per our help center guidelines). A better approach is to give details that characterize the publisher (as Kurt did quite well). This ensures that the question and answers will be applicable not just in this one situation, but also others like it.
There are appropriate resources for public "shaming." People can be directed to those sites as warranted.
The naming procedure itself is quite subjective and is not persistent, since the publisher/person might change and the question would be out of sync with real information. A rather more interesting question issued would be asking for guidance to identify the properties of a dodgy publisher/person. At this instance, giving out examples on naming a publisher/person doing (or not) a particular action would help on explanation.