Learn English – the “how” doing in one sense of the sentence “How would you like to die?”

When asking for a description of something, you should use the construction "What ... like?"

However, how is a perfectly valid question. It just doesn't ask for a description.

How seeks to learn:

• In what manner or way; by what means: How does this machine work?
• In what state or condition: How is she today?
• To what extent, amount, or degree: How bad was it?
• For what reason or purpose; why: How is it that he left early?
• With what meaning: How should I take that remark?
• By what name: How is she called?
• By what measure; in what units: How do you sell this corn?

etc...

When you ask "How is your new teacher?", you are not asking for a description. Instead, you are asking about her state or condition. The answer would involve adjectives like good, sick, happy, etc.

When you ask "How's the weather?", again, you are technically not asking for a description, but its state or condition. For questions like these, the distinction between "description" and "state" is pedantic, and you shouldn't worry too much about them.

To be more thorough about the "weather" questions:

Asking these questions will almost always get you the same (or similar answer):

• How's the weather?
• What's the weather like?

For example, I live in Southern Oregon, and the weather today is foggy and cold, so I might respond "Foggy and cold." The first question may also solicit "Not great. Foggy and cold." (And this is because how is asking about condition or state, something that what doesn't ask.)

However, if I ask "How's the weather usually in Toronto?" I'm trying to get a sense of weather or not the weather is "good" or "bad" usually, which probably isn't that useful. Instead, I would ask "What's the weather usually like in Toronto?", which would get me a description of the usual weather in Toronto (much more useful).

We are confusing and conflating these forms here:

1. How do you say ... (in X)? This is asking for a word or phrase, perhaps specifying in language X.
Example: *How do you say you're welcome in Hebrew? How do you say sandals in Japanese?*
2. What do you call … (in X)? This is asking for a word or phrase for something you're pointing at or describing. It may expect an answer in English, or in another language.
Example: *What do you call a helicopter in Cantonese? What do you call the blue thing on top of that box? What do you call that color? What do you call that color in French?*
3. How do you call … ? This is asking for a procedure: how do you call a waitress, a cat, a taxi. The expected answer can't be Toots, Felix, Yellow Cab.
4. What's ... name? This is asking for a noun word or phrase in the same language.
Examples: What's your name? What's the name of the movie you saw? 5. How do you ...? This question can take lots of different predicates, and the answers will all include verbs.

All these forms are good, grammatical, idiomatic English when used this way. Any other uses of these forms would be non-idiomatic, non-standard, and maybe incomprehensible.

The difficulty arises when foreigners use their own grammar and thought patterns, but with English words. Lei come si chiama? in Italian, literally means how do you call yourself? and does not expect the answer “I use a cellphone”. In idiomatic English this is what's your name? The Italian is wired to use this form for forms 2 and 4 above, never using the word “name” in questions like those. In fact, if an Italian pointed to something and asked another Italian what that thing's name is, he would be thought facetious, expecting an answer like “It reminds me of Sally, so let's just call it Sally for now.”

This difficulty cuts both ways. If you ask a Spanish speaker for his name, using form 4 above, you would say “Cual es su nombre”. He would be within his rights to answer “My name is the unique label by which I am distinguished from others in the room”. You should ask como se llama, but you're not wired for that, it's not one of the forms on our list.

So now to answer the questions.

What evidence is there that "How do you call..." is, or is not, a legitimate phrasal usage or expression in English? How do you call is legitimate in English – see form 3 – but only in the use allowed in form 3. Otherwise you do two things: you risk not being understood within the flow of speech, and you cause a needless proliferation of forms when we have a good one present already. I know this is getting into the descriptive-prescriptive debate, which is a different can of worms, but we're there anyway just by discussing the question. Your Ngram is all the evidence needed for pointing out that this is ono-standard. As for legitimate, well, that's an opinion.

Could it be called a dialectal variant? Why is it considered non-standard? These are two questions. First, no, I know of no such dialectical variant. Second, I have already shown why it's non-standard above. And indeed your Ngram shows that it's non-standard. There's another thing about Ngrams: in a world in which educational standards are dropping, along with IQs pace the Flynn effect, more and more examples of poor English are going to show up. Just because a form is standard in language A doesn't mean that it should become standard in language B, and this becomes very obvious when A and B are from different families.

Your final question pair:
How (!) do linguists define the "How do you call..." vs. "What do you call..." debate? Has any interest been shown in this lexical divergence between Romance languages and English?
The ! is unnecessary – this is a perfectly valid use of form 5 above. AFAIK, This debate doesn't have a name of its own – it's not important enough to deserve one.
The divergence between Romance and English here is not primarily lexical, but structural. As such, it's of prime importance in language learning – as you can see by the mistakes of those who haven't paid attention. Unfortunately, most language teaching starts with vocabulary to the exclusion of structure, so they teach the como se llama usted : what's your name equivalence almost as a single lexical chunk on each side of the colon, making comprehension and analysis of the structures very difficult for the learner. It would be far better if they used this as an early opportunity to teach that learning a foreign language is not just – indeed not even – a matter of word lists.