There are a lot of questions surrounding the Nei equipment. Where did it all come from? Why was it named after Nei? Why was it the only thing capable of stopping Dark Force? These questions are compounded by the fact that after Nei dies and Neifirst is defeated, neither of them are ever mentioned again.
For the second question, I'd assume that Nei is named after them, not the other way around. Dunno about the rest.
"Nei" is sort of a holy/power word, the Nei items are named that because they're sacred and that's why they work against Dark Force.