Since nobody answered, I thought I’d post an answer with what I’ve been able to find out myself
There is a list of 7 different neonicotinoid insecticides on Wikipedia:
Some say that Sulfoxaflor is also a neonicotinoid, but not everyone agrees with this.
The neonicotinoid insecticide that is most commonly used is Imidacloprid. I'm not sure if manufacturers are obliged to put the name of these substances on all their products, so these names might not show up on a product.
Bayer is the company that has invented Imidacloprid and also seems to sell the most products that have this stuff in them, so careful when buying stuff from them. Other brand names:
Admire, Advantage (Advocate) (flea killer for pets), Confidor, Conguard, Gaucho, Hachikusan, Intercept, Kohinor, Mallet, Maxforce Quantum, Merit, Nuprid, Optrol, Premise, Prothor, Provado, Turfthor, Temprid (Bayer), Winner, and Xytect (source wikipedia)
I also found this list with products that contain neonicotinoids, but there is no date so I’m not sure how old the list is and if it is complete (probably not).
The EU has decided that all countries have 1 year to start with the ban, so it’s possible that products with neonicotinoids in them are still being sold.
Apparentely there are many uses for neonicotinoids:
it can be applied by soil injection, tree injection, application to the skin of the plant, broadcast foliar, ground application as a granular or liquid formulation, or as a pesticide-coated seed treatment. (source: wikipedia)
I read that Imidacloprid is taken up by plants and trees and remains present in their flowers or seeds so I suspect there is no way of knowing for sure whether a tree, plant, flower bulb, or seed contains neonicotinoids without labtests. The safest choice is probably to buy organic plants, bulbs and seeds.