Most of the first paragraph of the entry seems to be a quotation or a paraphrase of some account from the first few centuries CE (perhaps an epitome of Pausanias 7.16.1-10), but the source is unidentifiable.
[1] So the transmitted text, both here and again at mu 565; but the Roman conqueror of Corinth in 146 BCE was L. Mummius (OCD(4) p.972).
[2] More specifically, the Romans gave the name "Achaea" to the province that they formed more than a hundred years later in the Peloponnese and central Greece. This province comprised some, but not all, of what was traditionally thought of as "Hellas". Prior to this, the term was generally restricted to the territory on the northern littoral of the Peloponnese (and is still used in that sense as late as the second century CE, by e.g. Pausanias (cf. Ptolemy 3.16.10)). The Romans responsible for naming the province may have been aware, however, that in Homer, the term "Achaiis" could refer to a much greater part of what was later known as Hellas (a term unknown to Homer) and that the "Greeks" at Troy could be referred to collectively as "Achaians". The Roman victory referred to here was not over "Achaia" per se, but over the Achaian League, which at that point included many non-Achaian cities, such as Corinth.
[3] Literally, "the whole name of the territory."
[4] This phrase is presented and glossed as if it were proverbial, but it is not in the paroemiographers.