Related: The Pascal's Wager Fallacy Fallacy, The Fallacy Fallacy
We need a catchy name for the fallacy of being over-eager to accuse people of fallacies that you have catchy names for.
When you read an argument you don't like, but don't know how to attack on its merits, there is a trick you can turn to. Just say it commits1 some fallacy, preferably one with a clever name. Others will side with you, not wanting to associate themselves with a fallacy. Don't bother to explain how the fallacy applies, just provide a link to an article about it, and let stand the implication that people should be able to figure it out from the link. It's not like anyone would want to expose their ignorance by asking for an actual explanation.
What a horrible state of affairs I have described in the last paragraph. It seems, if we follow that advice, that every fallacy we even know the name of makes us stupider. So, I present a fallacy name that I hope will exactly counterbalance the effects I described. If you are worried that you might defend an argument that has been accused of committing some fallacy, you should be equally worried that you might support an accusation that commits the Catchy Fallacy Name Fallacy. Well, now that you have that problem either way, you might as well try to figure if the argument did indeed commit the fallacy, by examining the actual details of the fallacy and whether they actually describe the argument.
But, what is the essence of this Catchy Fallacy Name Fallacy? The problem is not the accusation of committing a fallacy itself, but that the accusation is vague. The essence is "Don't bother to explain". The way to avoid this problem is to entangle your counterargument, whether it makes a fallacy accusation or not, with the argument you intend to refute. Your counterargument should distinguish good arguments from bad arguments, in that it specifies criteria that systematically apply to a class of bad arguments but not to good arguments. And those criteria should be matched up with details of the allegedly bad argument.
The wrong way:
It seems that you've committed the Confirmation Bias.
The right way:
The Confirmation Bias is when you find only confirming evidence because you only look for confirming evidence. You looked only for confirming evidence by asking people for stories of their success with Technique X.
Notice how the right way would seem very out of place when applied against an argument it does not fit. This is what I mean when I say the counterargument should distinguish the allegedly bad argument from good arguments.
And, if someone commits the Catchy Fallacy Name Fallacy in trying to refute your arguments, or even someone else's, call them on it. But don't just link here, you wouldn't want to commit the Catchy Fallacy Name Fallacy Fallacy. Ask them how their counterargument distinguishes the allegedly bad argument from arguments that don't have the problem.
1 Of course, when I say that an argument commits a fallacy, I really mean that the person who made that argument, in doing so, committed the fallacy.
I don't believe what's going on here is the sort of thing that should be called a 'fallacy'. Maybe it's a bias? A fallacy involves reaching a conclusion through invalid reasoning - whether we're dealing with a formal or informal fallacy, it's demonstrated by the possibility of true premises and a false conclusion.
Consider the following examples:
(A)
In this example 1-4 are premises, and this is a valid argument in sentential logic. However, depending on the understanding of the reader and the available rules of inference/replacement, it may be missing some steps. The conclusion comes from invoking the hypothetical syllogism 3 times successively, and the reader might not accept the hypothetical syllogism in the first place. However, in no case can premises 1-4 be true and the conclusion (5) be false.
(B)
This is an example of a formal fallacy; 1 and 2 are premises. It could be the case that q is true and p is false, which would render the premises true and conclusion false.
(C)
This is an example of an informal fallacy; 1 and 2 are premises. It could be the case that p is true, regardless of S's character. These fallacies can often be resolved by adding an additional premise, which makes the argument valid but shows that it is unsound. For example:
(D)
Here, 1-3 are premises. This might not be very helpful to its case, but now the argument commits no fallacy; it simply asserts (3) which is a false premise, so this argument is valid but unsound.
Now which of these does the 'catchy fallacy name fallacy' resemble? It seems to me that our two options are (A), where no fallacy is committed but the reader may need more explanation, and (C), where we're asserting that the arguer is leaving out a contentious premise.
I assert that most occasions of this phenomenon are more like (A) than (C), and so this should not be called a fallacy.
There's room for some confusion as to who commits the fallacy. If the speaker correctly classifies a mistake (that really is a mistake) as part of a category of structurally related mistakes, that's hardly a fallacy. The fallacy is, as you point out, taking a nice sounding label itself as evidence. Using quotes from famous people creates a similar danger.
I think there is a name for this effect, "association" or "framing" or something. But whatever.