Flora II (clearly aware of Koyama’s publications) uses the combinations in Baumeaand cites Koyama’s combinations in Machaerinaas synonyms.
Brummitt, R.K. (1992), Vascular Plant Families and Genera: 58; Goetghebeur, P. in Kubitzki, K. (Ed) (1998), The Families and Genera of Vascular Plants 4: 180-181, and Mabberley, D.J. (2008), Mabberley's Plant-Book Edn. 3.: 509; Flora of China etc. all have Marchaerinaas preferred name and Baumeaas a synonym.
NZ was the last country left still using Baumea,. All other countries have switched back over to Machaerina(Australia, Africa, etc.). Unpublished DNA data also supports putting Baumea and Machaerina together.
NZOR Concept Id
NZFLORA (2012-) New Zealand Plant Names - Name based concepts