Below I have selected a few plant genera beginning with the letters T, U and V 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
Tamarix - Derived from the Tamaris river in Spain where some of the species flourish. Tamaris is the Latin name and it has been suggested that it shares the same etymological route as the river Thames (Latin = Tamesis) which derives from an old Proto-Celtic name meaning "dark flow/river." In name terms its sound falls between Tamara and Beatrix.
Taxus - The ancient Latin name for the Yew tree derived from the Greek τόξον (toxon) "bow."
Theobroma - The genus of the cocoa tree, derived from the Greek θεος (theos) "god," and βρῶμα (broma) "food," (ala Ambrosia, 'food of the gods').
Thespesia - Derived from the Greek θεσπεσιος (thespesios) "wondrous, marvellous"
Tiarella - Derived from the Greek τιάρα via the Latin tiara, a name used to refer to the conical headdresses worn by Mesopotamian kings, alluding to the shape of the plants. Sound-wise it combines the popular names Tia and Ella.
Tilia - From the ancient Latin name for Lime trees.
Torreya - Named for American botanist John Torrey.
Tulipa - The Latin name for Tulip, derived from the Persian dulban "turban," which the plant is thought to resemble. Some interesting species names include: Cypria, Julia, Flava "yellow," Persica, Sylvestris.
Uniola - A diminutive of the Latin unio "unity."
Ursinia - Named after theologian Johann Heinrich Ursinus of Regensburg (1608-1666).
Valeriana - From the Latin valeo, "to be healthy," or possibly after the Roman physician Valerius.
Vanda - An orchid genus derived from the Sanskrit name of the first species introduced.
Vella - The cress genus. Derived from the Celtic name velar.
Velleia - Named for Major Thomas Velley (1748-1806)
Verbena - The Vervain flowers. The genus name is derived from the Latin name verbenae. The plants were sacred to the Romans who used them in religious acts.
Genera that were already personal names include: Thalia, Veronica, Vestia and Victoria.