The question asks about referring to people by nicknames. Is that English Language & Usage?
Is it English? Undoubtedly.
Now, Usage in “English Language & Usage” has a particular meaning:
7. a. The established or customary manner of using a language; the way in which an item of vocabulary, syntax, or grammar is normally used, esp. by a specified group or in a particular domain or region.
b. An instance of such language use; a word, phrase, construction, etc., used in a particular or characteristic way by a group, in a region, etc.
[OED, my emphasis]
Thus, using OED’s examples, one might ask about wagon as a verb, or pronouncing ask as /aks/, or how the expression my lover is used in the British West Country.
I’m not convinced that nicknames qualify in this case as “items of vocabulary, syntax or grammar.”
Is it Language?
I’m indebted to Kris who has reminded me just now of the question about Odin’s tears. That question concerned a particular turn of phrase,
The skies will burst open and Odin’s tears will drown the world of men on the day when...
which the OP was intrigued about. Asking about a metaphor (or any other device) is asking about the language. I reckon that question is on-topic — and indeed I answered it as being a colourful turn of phrase and gave a couple of interpretations. It matters not whether the speaker misremembered where in Norse mythology it came from, although it’s certainly useful to point that out.
Does asking about nicknames fall into the same category? Possibly: Yoichi’s question is buried a little, but it’s stated as
Is it a customary way of Americans to call dignitary’s names [sic] by an initial or an abbreviation like “W” and “Bar,” or is it just Ms Dowd’s idiosyncrasy?
The question asks about custom and practice when referring to people.
Is that Language? Or is it Etiquette? It’s borderline. In effect, the question is turned round from “What’s the best way of expressing contempt for a public figure in a newspaper column?” — and we have quite a number of “What’s the best way of...” questions.
SE has had a couple of attempts at a site on etiquette: One | Two. None of the example questions cover this aspect of public language, or even the “What’s the best way of...” questions, so it probably should be asked in ELU.
That said, focussing on a particular article and attempting to generalise from the particular is not a good form.