This name is a synonym of Brahea salvadorensis H.Wendl. ex Becc..
The record derives from WCSP
(data supplied on 2012-03-23)
which reports it as a synonym (record 460569) with original publication details: Gentes Herb. 8: 217 1951.
This name record (from WCSP) 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 Erythea cookii in version 1 of The Plant List.