Calathea or Goeppertia?

For the great majority of species in commerce, yes. Calathea G.F.W.Mey. (1818), as understood in the broad sense that prevailed through most of the twentieth century, is a synonym of Goeppertia Nees (1831) for most of its constituent species. The GBIF Backbone Taxonomy records Goeppertia Nees as the accepted name [3], while the horticultural trade continues to list the same plants as Calathea. The two names are not exact equivalents across all species: a small residual core — corresponding to subgenus Calathea Körnicke (1862), the Calathea lanicaulis group, and the formerly separate genus Sanblasia Andersson (1984) — continues to be placed in Calathea in a strict sense [2], while everything outside that core was transferred to Goeppertia by the 2012 revision [1].

Finn Borchsenius, Luz Stella Suárez Suárez and Linda M. Prince published the resolution in Systematic Botany 37(3): 620–635 on 1 September 2012 [1]. Their molecular phylogenetic analysis demonstrated that Calathea in the broad sense was polyphyletic: one clade containing subgenus Calathea and the C. lanicaulis group resolved as sister to a clade formed by Ischnosiphon and Pleiostachya, confirming that the old broad genus could not be maintained without rendering those other genera polyphyletic as well [1]. The paper published 246 new combinations effecting the transfers to the resurrected name Goeppertia Nees [1]. Subsequent combinations were added by Braga in Phytotaxa volumes 62, 167, 222 and 312 (2012–2017), addressing species overlooked in the 2012 treatment [2].

Goeppertia was originally described by Nees von Esenbeck in 1831 in Linnaea 6: 303–431; the genus name commemorates the German palaeobotanist Heinrich Robert Goeppert (1800–1884) [2]. Calathea was described by Georg Friedrich Wilhelm Meyer in 1818 in Primitiae Florae Essequeboensis, based on material from the Essequibo region of what is now Guyana [2].

The following names resolve to the same genus-level entity in this registry:

• Goeppertia Nees (1831) — accepted name, as recorded in the GBIF Backbone Taxonomy [3] and confirmed by the 2012 revision [1]. Name type: accepted epithet.
• Calathea G.F.W.Mey. (1818) sensu lato — genus-level synonym for the great majority of species, resolved by Borchsenius, Suárez Suárez and Prince (2012) [1]. Name type: synonym.

Calathea in the strict sense — subgenus Calathea Körnicke (1862: 112), the Calathea lanicaulis group, and Sanblasia Andersson (1984) — is retained as a distinct genus and is not synonymised into Goeppertia [2]. Marantaceae comprises approximately 550 species distributed throughout the tropics, with Goeppertia constituting the largest genus in the family following the 2012 revision [2]. No International Cultivar Registration Authority (ICRA) has been appointed by the ISHS for Marantaceae, Goeppertia, or Calathea; the published scope of the Heliconia Society International ICRA mandate covers several Zingiberales families but does not include Marantaceae [4].

In taxonomic literature published after September 2012, the accepted genus name is Goeppertia Nees, as established by Borchsenius, Suárez Suárez and Prince and confirmed in the GBIF Backbone Taxonomy [1][3]. In horticultural trade, the same plants are described and sold as Calathea. This registry records both names, their name types, and the authority responsible for the 2012 resolution. Genus names are governed by the International Code of Nomenclature for algae, fungi, and plants; the commercial prominence of Calathea in trade has no bearing on its accepted nomenclatural status, and no plant patent or cultivar registration attaches to either genus name.