I did a little digging.
Yes, that is the name you should use for your azalea. 'Azalea japonica'. This name is accepted in horticulture. It is the name of the plant.
This name is currently no longer in use by botanical taxonomists, but it is a name with historical and specific meaning. Your azalea is one of the Rhododendron section Tsuitsuisi species and hybrids. This is the larger group of species and hybrids that include the Satsuki hybrids, the Kurume hybrids, and other Tsuitsuisi hybrids. In 20 minutes I was unable to determine the current species name that would correspond to Azalea japonica, but I believe possibly Rhododendron kaempferi or possibly R. indica is possibly the current botanical name for Azalea japonica. At any rate, your plant is a species or most likely hybrid from the group of Rhododendron species found in Japan. All are section Tsuitsuisi species.
Somebody who is versed in Azalea history could look at the name an immediately tell you which species name is the current botanically accepted name.