Below I have selected a few plant genera beginning with the letter P 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
Paradisea / Paradisia - Named for 18th century count of Modena, Giovanni Paradisi.
Paralias - From the Greek παρα (para) "beside" and αλος (alos) "sea."
Patrina - Named after Eugène Louis Melchior Patrin, 18th century French traveller.
Paullina - Named after Simon Paulli, 17th century Danish botanish. Also Paulownia, named after Anna Paulowna, a princess of the Netherlands.
Pellaea- From the Ancient Greek πε λλος (pellos) "dark" referring to the dark stems.
Peltaria - From the Greek πε λτη (pelte) "shield."
Pereskia- Named for Nicholas Claude Fabry de Pieresc.
Perezia - After 16th century Toledan apothecary Lazarus Perez.
Persea - Ancient Greek name, given by Theophrastus, for an oriental tree.
Persica - From persicum the Latin name for peach, literally meaning "Persia" from where the tree was supposed to have come.
Petrea - Named after Robert James, Lord Petre, a patron of botany.
Phaius - From the Greek ϕαιός (phaios) meaning "dusky".
Philisia - From the Greek φιλεῖν (philein) "to love".
Phlox- From the Greek φλόξ (phlox) "a flame" alluding to the brightly coloured flowers. Next generation of Pax and Knox?
Pyrus - The classical name for pear trees.
Genus names that were already in use as first names include Paris, Pasithea, Philadelphus, Phoenix and Pleione.