Dear George; Please see Chapter 10, Article 48: ''Change of generic assignment'', and Article 34.2, about the need to have the gender of the species name in agreement with the genus gender (except for nouns in apposition, see Art. 34.2.1).
The transfer of a species from one genus to another is indeed the result of a taxonomic opinion. The Codes do not tell which opinion is appropriate. However, when an opinion leads to the creation of a new binomen, that creation IS a nomenclatural act. In particular, it may result in homonymy that did not exist before, with consequent need to abandon one of one of the homonyms.
It appears that zoological (in contrast to botanical) nomenclature neglects new combinations. There seems to be no tradition of recording (indexing) them, their date, place and authorship, contrary to botanical habit; nor am I aware of rules that govern their formation. This has some drawbacks, at least for databases; but with millions unrecorded such recombinations on hand, it is not likely to change.