From the standpoint of contemporaneity, I'm not sure with what confidence or on what criterion we may say that Earth is the "accepted" name of our planet, and with what limitations (i.e., in what linguistic spheres). Nor do I know where one could mark, and on what basis, a threshold past which that term had become "accepted".

But one distinction and criterion which it strikes me we may discuss, and must, from the point of view of historical lexicography on this question is the distinction between "Earth" as taxonomy for the realm of man and "Earth" as taxonomy for a planetary body located in orbit around the Sun of our planetary system.

I believe this is an important distinction, as "Earth" (Old English eorþe) has been in commonplace English use as a term for the realm of man since at least the 7th century. In the Old English context, it does double duty, somewhat as it does modernly, sometimes connoting land (in contrast with sea - ever significant to the lexical substance of the North Sea Germanic languages), and sometimes connoting the realm of man generally, from the standpoint of religious cosmology. It is more common than the (ironically) somewhat better known "middangeard" (likewise connoting the realm of man) in this cosmological role, in those religious texts which reference cosmology, such as Genesis A and B, Cynewulf's Christ II, and Caedmon's Hymn. Though the latter term usually appears in these as well.

But to name the realm of man, between heaven and hell, is not strictly speaking to name the planet on which we stand, whether we believe we abide in one or both, and that's the distinction which I think would need to be addressed, to properly contend with this question.

As for the word itself, the place of "eorþe" as the material world in which we live was strongly established in the doctrinal theology of the English-speaking world (in its drastically lesser Early Medieval extent), and hence the scholarly language of that world, very early indeed. To the extent that the 7th to 10th centuries had authorities who might agree on the name of our place in the universe, its name was indeed "eorþe", more than any other.

The transition to an astronomical connotation was not a shift in usage or even meaning so much as it was a shift in the cultural context and conceptual framework through which that meaning was interpreted. And consequently, it is exceedingly difficult to address that in lexical terms. I suppose that a historian of science could best address that shift in conceptual framework.