The genus (or first part of the scientific name) for bougainvillea is actually "bougainvillea." There are several species, including Bougainvillea glabra, which if you are in the southern United States, this is most likely the horticultural species you will find.
If in South America, there are species called Bougainvillea peruviana and Bougainvillea spinosa.
Bougainvillea glabra