Consider the brief passage:
"I love your work, but calling you 'the artist' {1} just doesn't seem to be cutting it anymore. What shall I call you?"
"OK. Call me George." {2}
So my instincts tell me to put {1} in single quotes as opposed to no punctuation (or perhaps even italics) but to do the opposite for {2}. Is this right? Why?
Let me expand this one further iteration:
"Wow, that's a great name, especially with this crowd. Maybe for your next book you should call yourself Ringo."{3}
Clarity is the point of typography.
Personally, I like the literal quoting scheme, where quoted sections are punctuated as normal, excepting only the double and singles toggled for nesting. It's rather common to collapse final punctuation when the outer sentence and quoted sentence agree.
E.g. "I love your work, but calling you 'the artist' just doesn't seem to be cutting it anymore. What shall I call you?"
"OK. Call me 'George'."
As to why it seems different, I suggest it's because "Call me George" fits a pattern of use for "call" that isn't actually spoken, so would not be quoted. ("Call me later." "Call me off.")
Alternately, some schemes would skip quoting it simply because it's not, literally, a quote: It's an imperative to speak.
I would quote the called-out term, "George", since that clarifies the use of the word "call" in the sentence. (used as 'use the following in speech' rather than as a shorthand for 'describe as')
(Ed. It bears noting that simply capitalizing the word "George" calls it out as a proper noun, which grants it special distinctions.)
The typographic rules you should follow should be clear but also fit any rules established by a relevant authority; (publisher/teacher) Do realize that there are multiple competing conventions.
Nowadays, we often use quote-like structures for report structures, with the same verbs, so I would argue that the following are all quite acceptable:
She wished him "Happy Birthday!" [salutation capitalised for emphasis as with a title]
She wished him Happy Birthday. [report structure mimicking quote structure]
She wished him a happy birthday.
...
She wished him "Merry Christmas and a Happy New Year!"
She wished him Merry Christmas and a Happy New Year. [report structure mimicking quote structure]
She wished him a merry Christmas and a happy New Year.
...
'OK. Call me "George".' (cf 'Just use/say "George" when we're off duty.')
'OK. Call me George.' [report structure mimicking quote structure]
This question brings to the fore an indubitable discrepancy.
Why should we find such phrasing as "They called him "John E.", and alongside sentences such as "They called him John."? (In this same book we also find "They called him John E.".) The plain answer is that English is not always consistent as regards the logicality of the forms used. So your instinct is right as regards current practice ("They called him John." is the standard form), but it is wrong insofar as that form is not the logical one.
Language is a means of representing in your mind, first of all, reality, but also fictive reality (lies), and fiction (hypothetical reality). This means that each word in an utterance has the role of representing an entity which is interrelated to some of the others in the sentence through the agency of grammatical rules, meanings, and contexts.
Put differently, the word in the sentence has the role of signifying something, that is, the role of being a sign or symbol for something, or, equivalently, the role of denoting something, but something that is always different from the word itself. This role is not limited to the sentence but is also real when the word is considered by itself. This denotation is not necessarily unique and it varies according to the context of occurrence of the word. For instance, in a dictionary of personal names, the word "John" denotes an indefinite person among all the persons who have received that name. In the context of a text about the former president of the US, John Fitzgerald Kennedy, and especially in this three word name, the denotation is unique, so when we see this word in that text, it being clear that no other person named John figures in the story, we can be certain that the president (or president to be) is the person implied, or, in other words, signified. In exceptional sentences this word, modified, may even represent all the persons named John.
(Wikipedia, signified and signifier) In semiotics, signified and signifier (French: signifié and signifiant) are the two main components of a sign, where signified is what the sign represents or refers to, known as the "plane of content", and signifier which is the "plane of expression" or the observable aspects of the sign itself. The idea was first proposed in the work of Swiss linguist Ferdinand de Saussure, one of the two founders of semiotics.
Words usually appear in sentences uniquely as signifieds; this principle is true for all words, but sometimes it is needed to introduce words in a sentence in such a way that their role of signifying something is cancelled, that is, we need to consider them as the thing itself used to signify something, in other words, as signifiers. One important role of quotes is to suppress the role of normal representation of a word, that is to stand for a signified, and replace it by a self-representation.
She wrote it on the board. ("It" has the role of standing for something that was mentioned before, and that something is now written on the board; it is what "it" as a signifier represents.)
She wrote "it" on the board. ('"It"' does not have the role of standing for something that was mentioned before; what has been written on the board is now the word "it".)
Cases not involving the idea of double representation found in the preceding two examples ("It" has the role of representing an abstract entity (pronoun) that has for grammatical role that of replacing a noun phrase or an idea, which replacement is tantamount to representing the entity that corresponds to the noun phrase, or representing the idea if an idea is involved.)
They said that John is a nice one. (John is one of the teachers; "John" represents a human being.)
They said that "John" is a nice one. ("John" is a nice name. '"John"' does not represent a human being.)
It can be seen that the change in the representation forces a change in the category in which the pronoun can find a replacement; in the first sentence the category is that of the words that are defined as describing a sort of person (man, grand-father, adult, member of a club, professional, …), in the second it must be the category of words that are defined as naming a person (surname, nickname, middle name, last name, alias, …). In the first sentence, "John" stands for someone, a given person, either real or fictitious; that person can be visualized according to the idea that one has conceived of them in the particular context of the utterance; in the second, there is no given person being represented by '"John"', no such visualization possible; we are dealing in that sentence with the signifier, and to remain consistent with this principle, quotes should be used.
Why the principle is not applied for "call me George" whereas it is applied for "calling you 'the artist'", I would say, is a matter of habit that has various uncertain roots; for instance it is important to make clear that "the" is part of the name and quotes appear convenient for the purpose of grouping, although they are not used for that.
In "OK. Call me George.", "George" stands for nobody because the action of the verb has nothing to do with a person named George; it impinges on the person referred to as "me", who might very well be named George; in this latter case, crude but approximately exact replacement would result in "Call George George.", which, incidentally, tends to shows the different linguistic natures of these two words each written as "George".
My usage above ("named George") is corroborrated by the findings in Google Books, where of all the occurrences of "named John", only one is properly written 'named "John"'.
Two cases of 'called "John"' can be found.
The Gospel of John - Francis J. Moloney, Daniel J. Harrington · 1998.
Addresses of the Mississippi Philosophical Association - 2021
According to the OALD (2005), the construction 'Call me "George."' is entirely similar to that in the sentences
in which the verb is acknowledged as a transitive verb, where "him" and "it" are the objects and "MP …" and "wiser plan …" are the object complement. The fact that the noun "George" is between quotes does not change the grammar and is entirely a matter of semantics.
