This circumpolar plant has one scientific name, Lonicera caerulea, but as common names go, there are several things to call this hardy shrub that bears tasty blue fruit. According to University of Saskatchewan, the breakdown of common names is as follows:
Haskap – for L. caerulea of Japanese descent. There are several iterations of this name, including Hascap and Haskapa. One account attributes the name Haskap as being a modification of hashikahpu, the Japanese word for the fruits.
Blue honeysuckle – translation of the Russian name for L. caerulea. Russian varieties tend to flower earlier than Japanese varieties.
Honeyberry – a name coined by Jim Gilbert of One Green Earth nursery in Oregon.
This website (haskapa.com) has the most complete origin information that I have seen so far, as well as this write-up from Dr. Bob Bors at University of Saskatchewan.