The Treatise on Invertebrate Paleontology volume on bivalves has an extended discussion on this issue (p. N3-N4).  Bivalvia was used at least by 1681, and Linnaeus used the term more or less as referring to the class of mollusks as presently understood (he had Teredo with worms and a few brachiopods with the bivalves).  Bivalvia has been used in several influential references, and seems to have the greatest popularity.  Dr. Pojeta is probably the most prominent advocate of an alternative name.  Pelecypoda and Lamellibranchia suffer from the opposite problem-many do not have an axe-like foot or plate-like gills; in fact, Lamellibranchia is sometimes used to refer to a subset of the bivalves.  Rare examples of shell reduction in the bivalves (Xenoturbella and a dwarf male galeommatoidean) provide exceptions to that name, too.

    Dr. David Campbell
    "Old Seashells"
    Biology Department
    Saint Mary's College of Maryland
    18952 E. Fisher Road
    St. Mary's City, MD  20686-3001 USA
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"Mollusks murmured 'Morning!'.  And salmon chanted 'Evening!'."-Frank Muir, Oh My Word!