Nomenclature for polymers and other macromolecules is traditionally an area of frustration. It is impossible to have a systematic naming as we know it from the small molecules, except for a few simple polymers, so nomenclature in these cases reflect a pragmatic solution to names, as it is done in real life practice.
Though you cannot make systematic names for macromolecules as we know them from the small molecules, we do have a systematic approach to the names, that is used in practice. Problem is, that people are not using the same system, which can lead to some misunderstandings. There is no inherent right or wrong in choosing one system or the other, but there is systems that are more suitable than others, depending on the situation. Seeing several of the described ways of naming at the same time, when communicating, is not uncommon, so the various ways of naming macromolecules is not one or the other, but options used according to need.
Naming according to monomers
Naming macromolecules according to the monomers is the closest thing we have to systematic naming. In the simplest versions we have polymers like polyethylene and polypropylene, where there is no doubt about the monomer sequence or linking between monomers, at least in principle. If you have optic isomers in the monomers, and you can control this in the synthesis, you also specify this, e.g. an isotactic polypropylene.
If you have an alternating copolymerer, you can write this, e.g. poly(hexamethylenediamine-co-adipic acid). Similarly you can refer to the linking, if this is relevant, e.g. poly(1,4-β-D-glucose) and poly(1,4-α-D-glucose), cellulose and amylose respectively, where the ether bond between C(4) in the first momoner and C(1) on the next is oriented in the α or β direction relative to the C(4) position.
For mos polymers, naming accoring to monomers is not very precise. You mention the monomers, but architecture and ratio between monomers is left out. Inappropriate naming of monomers adds to the minunderstandings. The copolymer PET it written as poly(ethylene-therephthalate), but the ethylene is not ethylene but ethylene glycol. A rubber type like EPDM, is an abbreviation of poly(ethylene propylene diene methylene), which could be perceived as a polymer consisting of four monomers. Polymethylene however, is just a another name for polyethylenen, so mentioning it is actually redundant. Diene in EPDM can be three different monomers, which will have an effect on the polymer's properties, and you have no way of knowing which one is used in a particular type of EPDM rubber. So: what sounds like a systematic name may not be so.
Naming according to the linkage between monomers
Naming according to how the monomers are linked is widely used, and at the same time a poor description of the polymers properties and application areas. No distinction is made, whether it is the resulting bonds or the polymerization process, the name refers to. So, you have epoxies, referring to a functional group in the polymer synthesis, and polyurethanes, referring to the resulting links in another polymer synthesis. The name describes how the monomers are linked, not the type of monomers being linked, thereby revealing very little about the material's properties.
There is three valid reasons for using this approach, when naming polymers.
Trade secrets. If you do not mention which monomers are in there, it is harder to copy the product.
Expectations regarding properties. Polyurethanes, for instance, are generally resistant to abrasion and have high tensile strength. Polyesters should not, among other things, be used in alkaline environments.
Safety in use. If you need to do an in-situ polymerization, e.g. epoxy paint, the requirements for safety equipment are different from using a paint where the binder is an emulsion in water.
Naming the macromolecules according to the linkage between monomers is thus not a bad idea, quite the opposite, it just does not provide much information about the molecular architecture in the macromolecure.
The use of common names is a surprisingly efficient way of having unambiguous names. It requires a good deal of knowledge about polymers, which takes time to learn, but combined with the name of the modification, if present, it is a highly efficient approach in practice.
Common names are names like cellulose and pectin, where the name and source, e.g. pectin from citrus peels, provide a plethora of implicit informations about monomers, properties, purities etc. If you have derivatives, e.g. carboxymethylcellulose and carboxymethylinulin, you immediately have a sense of differences and similarities for the materials, provided you know your polysaccharide classes and modification types.
Common names are primarily used for natural and semisynthetic polymers, but a few synthetic polymers are so widely used, that the abbreviations have become the name people use, though it might lead to misunderstandings. Polyethylenglycol is usually just called PEG, and a PEGylation is thus a PEG sidechain attached to another molecule, and a monomethoxylated PEG, is a PEG, where one of the alcohol groups at the end of the chain is modfied with an methoxy group.
Tradenames are widely used in production plants. In regards to communication, especially between coworkers with no understanding of chemistry, or a sense of material properties and function, tradenames are excellent for naming the material. Tradenames however, rarely reveal what kind of material you are looking at, and it may cover more than one material. A widely used material like Viton is three different types of fluoropolymer, with different properties. There is nothing in the tradename telling you that the material is a fluoropolymer, or which one of the three types of fluoropolymer it is, so you cannot just replace one type of Viton with another.
There is a few polymers, where the tradename refer to one specific polymer, produced only by one company, where you can argue that the tradename cannot lead to misunderstandings, but it is fairly uncommon.