The blue berries are edible.
Note that the name Honeyberry is also used for some different unrelated fruits.
Names
Scientific
Lonicera caerulea
English
Blue honeysuckle
Blue-berried honeysuckle
Haskap
Honeyberry
Sweetberry honeysuckle
Spanish
Madreselva azul
French
Chèvrefeuille bleu
German
Blaue Doppelbeere
Blaue Heckenkirsche
Taxonomy
Order
Dipsacales
Family
Caprifoliaceae
Genus
Lonicera
Species
Lonicera caerulea (Blue-berried honeysuckle)