Q. What is the proper way to write a botanical name (Latin name)?
It is interesting that although the question refers to botanical names as "Latin" names, in fact, many of them are Greek in origin. The term "Latin names" comes from the fact that all names, i. e. originating from Latin, Greek, other languages, place names and people's name, etc. are declined following the rules of Latin grammar..
Although botanical nomenclature is rather complicated the way to write these names is fairly straightforward..
Genus and species: Names should always be italicized or underlined. The first letter of the genus name is capitalized but the specific epithet is not, e.g. Lavandula angustifolia. If the meaning is clear, the generic name can be abbreviated, e.g. L. angustifolia.
If the specific epithet is not known or not needed then it can be indicated by sp. (or spp. plural), e.g. Rosa sp.
Authority name: In botanical journals and texts the specific epithet may be followed by the name of the person responsible for naming the species. This name should not be italicized, e.g. Arum masculatum L., where L. is an abbreviation for Linnaeus.
Ranks below species (indicating natural variants) are also italicized but the connecting term e.g. subspecies (subsp.), forma (f.) or variety (v. or var.) is not italicized, e.g. Salvia microphylla var. wislizenii.
Synonyms: Some plants have two accepted names In this case, the less-used name is indicated by syn. (Roman font), e.g. Senna alata (syn. Cassia alata)
Cultivar names (indicating variants selected or derived by gardeners): are not italicized. They can be indicated by cv. or placed in single quotation marks, e.g. Sansevieria trifasciata cv. Golden Hahnii or Sansevieria trifasciata 'Golden Hahnii'. The first letter(s) in each cultivar name is capitalized.
Hybrids (either natural or derived by gardeners): can be indicated by an "x", also not italicized. Both the genus name and the specific epithet are italicized, e. g. Platanus occidentalis x Platanus orientalis. Sometimes the hybrid is given a new name: Platanus x acerifolia, in this case.
Note that orchids tend to have their own style of nomenclature, e.g. the generic name can be abbreviated and the "x" omitted. The generic abbreviation is italicized.
Grex: Grex names are largely confined to orchids (the term refers to seedling derived from a hybrid cross). The grex name is written in Roman font, e.g. Pleione Fujiama 'Teal', where Fujiama is the grex name.
Trade names: Some cultivars have trade names or trademarks. These should be styled in a different font, e.g. capital letters or with a ® for registered trademark or ™ if they are trademarked.
Family names: There is some confusion as to how family names should be written. In American usage the family name is not usually italicized, e.g. Pinaceae, however the most recent edition of the International Code of Nomenclature for algae, fungi, and plants (which is the official authority on plant names) recommends that all plant names be in a different font from the rest of the text. The Royal Horticultural Society (U.K.) recommends that family names be italicized. Plant labels in botanical gardens usually have the family name in capital letters, e. g. PINACEAE.
Common names: There are no rules governing common names but it is standard usage to write the names in lower case except when naming a cultivar and to use Roman fonts.
http://www.iapt-taxon.org/nomen/main.php (The International Code of Nomenclature).
http://harris.agrilife.org/files/2011/05/RHSnomenclature.pdf (RHS recommended style).Courtesy of NYBG Plant Information Service