Species of Styphnolobium were formerly classified as being in the genus Sophora. Both the Sophora japonica and Styphnolobium japonicum names have been used for this species. The latter appears to be the current name. Many plants have been reclassified in recent decades due to genetic studies so a lot of scientific names have been changed.
The 'Pendula' name for this cultivar (which means an artificially created variety) refers to the pendulous branches and is a common name for horticultural varieties that are weeping. As I understand it, "pendulum" would be the grammatically correct form to go with the new species name, but this part of the name does not appear to have been updated in all cases.
Excellent images, especially the first one.