Each method has its own merit and should be used when appropriate. Historically and traditionally, polymers have been named by attaching the prefix "poly" to the name of the real or assumed monomer. The simplest examples are polystyrene, poly(vinyl acetate), poly(methyl methacrylate), and copoly(styrene/methyl methacrylate). Most papers published in macromolecular chemistry journals have such names in their titles, and most indexing systems are based on such names, including monomer-based, albeit somewhat reformatted and systematized, names in the indexes to Chemical Abstracts (CA) and to encyclopedias such as the Encyclopedia of Polymer Science and Engineering.
In the course of polymerization, however, reactions occur and the reactive sites, be it a double bond, a terminal amino group, or a carboxy group, are no longer present in the final product. Therefore, in order to reflect the structure of the polymer, for regular polymers (i.e., those which have only one species of constitutional repeating unit in a single sequential arrangement), a new method of naming was devised by the ACS Polymer Nomenclature Committee back in 1968,(2) which was subsequently adopted by the international Union of Pure and Applied Chemistry (IUPAC).(3)
Here are some examples of the structure-based nomenclature applied to selected polymers described and illustrated in the April 1992 issue of Polymer Preprints. Each structure has been oriented according to the predetermined seniority and order of the constitutional subunits, and each such subunit named as a bivalent radical according to the rules for organic nomenclature.

poly(imino-1,4-phenyleneiminocarbonyl-1,4-phenylenecarbonyl)

poly[2,5-thiophenediylcarbonyl-2,5-thiophenediyloxy-1,4-phenylene- (1-methylethylidene)-1,4-phenyleneoxy]

poly(benzo[1,2-d:5,4-d']bisoxazole-2,6-diyl-1,4-phenylene)

poly[(methylvinylsilylene)trimethylene] or poly(1-methyl-l-vinyl-l-silatetramethylene) (the "replacement" nomenclature, however, is not recommended for chains with one hetero atom only)
REFERENCES
1. Metanomski, W. V. "Nomenclature Note No. 1". Polym. Prepr, (Am. Chem. Soc., Div. Polym. Chem.) 1991, 32(1), 655-656.
2. American Chemical Society. "A Structure-Based Nomenclature for Linear Polymers". Macromolecules 1968, 1, 193-198.
3. International Union of Pure and Applied Chemistry. "Nomenclature of Regular Single-Strand Organic Polymers". Pure Appl. Chem. 1976, 48, 373-385. Reprinted as Chapter 5 in "Compendium of Macromolecular Nomenclature". Blackwell, Oxford, 1991.
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* Mailing address: Chemical Abstracts Service, P.O. Box 3012, Columbus Ohio 43210.