Attempting to find a set of possible relationships between things and words, I have come up some ideas. The first postulate (as per Saussure) is that names are arbitrary; however, this does not negate the possibility that names can be assigned which create relationships between the thing and the word that names it. Discounting purely arbitrary names for the moment, it seems likely that:
Names can be related to the names given to other things which bear a resemblance to the thing [substantive rather than phonetic homonymy— metonymy is a better term].
Names can be related to the names given to other things which bear a similarity to the thing [qualitative synonymy—metaphor is a better term].
By definition, homonymy and synonymy are mutually exclusive. However, in some literary and linguistic definitions, metonymy is not exclusive of metaphor—in fact, metonymy is thought to be a subset of metaphor. This relies on a broad definition of metaphor as “transfer of meaning.” However, if metaphor is defined as a rupture with standard usage—a rupture at the substantive level—then being contiguous with its subject, metonymy cannot be of the same genus as metaphor. Separating these two terms and casting aside that classical hypothesis there are unique “god given” proper names for things creates a new grid of possible names.
Paronymy, a category of derivation, is equally open to the axes of metaphor and metonymy. A name can be paronymous if it takes its root from a metaphoric name or a metonymic one. Synecdoche (substitution of a part for the whole, or the converse) can also draw equally from the same categories— or from an arbitrary name. The two terms hold in common a distance from the original name—a derivation. In synecdoche, there is a consonance with another name which is either substantive or qualitative.
Irony now seems to me to be the opposite of paronymy. Rather than consonance, what seems to be at work is a tension created by the inversion of meaning at either the substantive or qualitative level—a dissonance. The only thing I have not been able to figure out is if a paronym can be ironic in the same way a metaphor or metonymy can. I can’t think of any ironic paronyms offhand. I also cannot think of any “rules” which would exclude an overlap with paronymy in the same way that metaphor and metonymy are exclusive.
Rather than forming a stable triad like the basic Aristotelian relations, naming conventions seem to follow a shaky quadrilateral. Closing the gap in the center seems possible (language can be internally consistent without being consistent with the external world of things). It looks like a weird sort of flower.
I am more confident of this sort of arrangement than trying to envision irony as some sort of overriding category of negation. Somehow, it seems impossible to deal with conventions of naming without dealing with irony. There certainly are ironic names.