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)
1. p→q
2. q→r
3. r→s
4. s→t
5. ∴ p→t

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)
1. p→q
2. ¬p
3. ∴ ¬q

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)
1. S has argued that p
2. S is a bad person
3. ∴ ¬p

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)
1. S has argued that p
2. S is a bad person.
3. if S is a bad person and S has argued that p, then ¬p
4. ∴ ¬p

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.