Much like people, plants are given two names. The first is the general group name, like a surname, or genus of the plant. The second, as with our first names, defines the individual plant in the genus by its species. This system was devised by Caspar Bauhin (1560-1624) and adopted by Swedish naturalist Carl Linnaeus (1707-1778), which was a great improvement on the wordy sentences plants had previously borne.
The majority of plant genera are derived directly from Latin, and by extension, Greek. Several have also been borrowed from human names; some from Greek mythology and others after more modern namesakes.
I have selected a few plant genera beginning with the letter A, along with any of their interesting species names, that I think could have potential use as a name choice for any nature-loving family.
Abelia - A flowering shrub named after Dr. Clarke Abel.
Abies - Fir tree, from the Latin abeo "depart" possibly referring to its height from the ground. One of its species amabilis derives from the Latin for "lovely".
Abronia - Long-stalked fragrant flowers, from the Greek abros meaning "delicate".
Acacia - Already found used occasionally on girls, Acacia is a genus of shrubs or trees whose name is derived from the Greek ake "thorn". One of its species, found in Australia, is called baileyana (commonly Cootamundra Wattle) after Frederick Manson Bailey.
Acanthus - From the Greek akanthos meaning "prickle". One of the species, mollis, is from the Greek meaning "soft, delicate" and could be used as an alternative to Mollie.
Acer - The scientific name for maple trees, from the Latin word meaning "hard" or "sharp". The wood was used for writing tablets. Could possibly be used as a nature-derived alternative to Asa.
Achillea - Commonly known as yarrow and named for Achilles in Greek mythology who was said to have used the plant to treat wounds. It's species include alpina "of the Alps" and montana "of the mountain" and rupestris "by rocks".
Actaea - Believed to be either from the greek aktea "elder" or aktara "elm" due to similarities with the leaves. Actaea / Aktaia is also found on a Nereid and a Danaid in Greek mythology whose name meant "of the shore." Alba is one of the species, named so for its white berries.
Actinella - From the Greek aktis meaning "ray, sunbeam" -- literally "little ray (of sunshine)" -- as the flowers are rayed like little sun-flowers. Actinotus is a genus that derives from the same meaning.
Agathaea - From the Greek agathos "good" in reference to the plants beauty. Coelestis "heavenly, sky" is one of its species.
Agave (pronounce the last 'e') - Commonly known as century plant, agave derives from the Greek aganos "noble"
Alisma - An aquatic plant. Its meaning is unknown. The Irish called it the "leaf of Patrick" and it was said to ward off faeries.
Allium - The onion genus. Allium was the Latin term for garlic, or the name could derive from the Celtic all 'burning, pungent'. One of its species is the rather nicely named roseum "rosy".
Aloysia - Named after Maria Louisa, Queen of Spain. Citriodora is a lemon-scented species.
Arabis - The Greek name for Arabia, from where several species are found. Albida "white", lucida "shining" and petraea "of rocks" are among its species.
Aralia - Herbaceous plants whose etymology is unknown.
Arum - A flowering plant. Possibly from the Arabic ar "fire". Close in sound to Arran and Arun.
Aster and Astrantia - Two star-like flower genera, derived from the Greek word for "star".
Aubrieta - Named for M. Aubriet a French botanical artist.
Azara - Evergreen shrubs named after J.N. Azara.
Azolla - A floating aquatic plant, literally meaning "killed by dryness" in Greek in reference to its water-type.
Some names of genera that were already (non-nature) first names include: Ada, Althea, Andromeda, Angela and Artemisia.