This name is a synonym of Eubotrys racemosa Nutt..
The record derives from WCSP (in review)
(data supplied on 2012-03-23)
which reports it as a synonym with original publication details: Bull. New York Bot. Gard. 1: 284 1899.
This name record (from WCSP (in review)) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Leucothoe elongata in version 1 of The Plant List.