I have selected a few plant genera beginning with the letters G, H, I and J, along with any of their interesting species names, that I think could have potential use as a name choice.
Plant names:
A I B to C I D to F I G to J I K to M I N to O I P I R to S I T to V I W to Z
Gilia - Named after Spanish botanist Felipe Gil. Gilia was used as a feminisation of Giles in the Middle Ages.
Gillenia - Arnold Gille was a German physician who wrote on horticulture in the 17th century.
Gloriosa - Tropical climbing plants, from the Latin word meaning 'glorious'.
Greyia - Named after Sir George Grey, explorer and governor of South Australia. As a name it is very close in sound to the Manx name Graihagh, meaning "lovable".
Haberlea - Named after botanist Carl Constantin Haberle.
Halesia - Commonly known as Silverbell or Snowdrop tree and named after botanical author Dr Stephen Hales. Carolina is a species name.
Hedera - The Latin name for Ivy. Cypria and Helix are species names.
Heliophila - Delicate blue flowered plants, derived from the Greek helios 'the sun', and phileo 'to love'.
Hesperis - From the Greek hesperos 'evening' as the purple or white flowers are often more fragrant at that time. Aspera (L. "rough"), Kitiana and Persica (G. "Persian") are species.
Holcus - "Soft grass", the genus of eight species of grass. Derived from holkus, the Greek name.
Idesia - A flowering plant native to East Asia, named after E.Y.Ides, a Dutchman who travelled to China in the 17th century.
Ilex - The holly genus. The Latin name is derived from Quercus Ilex (Holm Oak) which was thought to resemble holly. Species include Amara (L. "bitter"), Cassine, Collina (L. "hill"), Corallina (L. "coral"), Perlata (Med L. "pearly").
Inula - Considered to be a Latin corruption of the Greek helenion. The name relates closely to Helen in Greek mythology, and several myths associate the flower to her. It was often written as Enula by medieval writers.
Itea - Derived from the Ancient Greek name for the willow, as the leaves are considered to be similar.
Ixia - Commonly known as the Corn Lily. From the Greek name for birdlime, in reference to the plants' sticky nature.
Ixora - Commonly believed to be derived from Iswara, the name of a Malabar deity to whom the flowers were dedicated.
Jacaranda - Tropical trees native to South America with vivid purple foliage. Believed to be derived from the Tupi name referring to the trees' hard wood.
Jamesia - Named after American botanist, Dr Edwin James.
Hebe and Ismene are plant genus that take their names from characters in Greek mythology.