Unless the plant’s scientific name and common name is the same, the common name should be lowercase, roman.
In common names that include a proper noun, capitalize the proper noun:
Copy editors should question common names when they find discrepancies; however, many plants have more than one common name, and the choice of which common name to use is at the editor’s discretion.
Some plants share common and scientific names. They may appear as lowercase and roman when the usage is common, or they may appear with caps and italics when the usage is botanical, at the editor’s discretion. Here are some examples:
Some names designate different plant genera when used commonly or scientifically. Therefore, it’s best to clarify them on first reference by using both common and scientific names. In subsequent references, capitalize and italicize when referring to genera and lowercase and romanize when referring to the common name.
azalea (Rhododendron spp.) or rhododendron (Rhododendron spp.)
bacopa (Sutera cordata) or water hyssop (Bacopa spp.)
blue mist spiraea (Caryopteris spp.) or spiraea (Spiraea spp.)
cranesbill (Geranium spp.) or geranium (Pelargonium spp.)
chrysanthemum (Leucanthemum spp.)
vanilla: extract of beans from the Vanilla vine, which also produces orchids