Informal fallacies are not formal, so as might be expected, there exists no prevailing standard taxonomy. Various books on logic and logical fallacies organize fallacies differently, (see chapter headings), and each reorganization constitutes its author's own partial taxonomy. Online one attempt at a more complete taxonomy exists at fallacyfile, while O. M. Williamson offers a lively but less rigorous taxonomy that proposes various opposite pairings.
Programmers call their ad hoc taxonomies data structures, and programmers almost always name these structures, which helps when distinguishing between differently organized structures made of identical data elements.
Taxonomies of fallacies don't seem to have names, so that sometimes one sees squabbles, (perhaps from students who studied from different books), discussing whether fallacy N is the child, parent, or cousin of fallacy X. Such students lack a vocabulary by which to more easily distinguish between differing taxonomies, the better to help upgrade those squabbles into more useful comparisons of the pros and cons of favored taxonomies.
Are there widely used names for the most common taxonomies of informal fallacies?
Lacking that, what attempts have been made at proposing names for those taxonomies?
Failing that, how should such taxonomies be named, or perhaps categorized (into meta-taxonomies)? Author names, principle branches of a taxonomy, distinguishing properties of a graph structure, acronyms, etc. come to mind.