In BfA there's two new Lua API namespaces for Azerite items.
The necklace is considered an "Azerite Item" and is under the C_AzeriteItem namespace, see /api AzeriteItem
The other pieces that are powered by the necklace are considered "Azerite
Empowered Items" and are in the C_AzeriteEmpoweredItem namespace, see /api AzeriteEmpoweredItem
To answer your question on the name, this is how Blizzard does it.
Code:
local azeriteItemLocation = C_AzeriteItem.FindActiveAzeriteItem()
if azeriteItemLocation then
local azeriteItem = Item:CreateFromItemLocation(azeriteItemLocation);
print(azeriteItem:GetItemName())
end