In Fairy Tail, all the Dragons have names, like the Fire Dragon, Igneel. But I don't remember anyone mentioning the names of the Thunder Dragon or the Poison Dragon in the anime. Does someone know what their names are?
Laxus and Cobra are Second generation Dragon Slayers, so they weren't taught Dragon Slayer Magic by a Dragon. Hence, Thunder and Poison Dragons are never mentioned (moreover, they possibly do not exist at all).
Those from the second generation of Dragon Slayers have had Dragon Lacrima implanted into their bodies, granting them the ability to use Dragon Slayer Magic. Because they were not taught their abilities by a Dragon, they are considered artificial Dragon Slayers.