All drugs have different names. There is a generic name and a trade name (and probably others as well). The trade name is simply a brand name. Its what different companies call the drug. The generic name is usually the long chemical name that few people can say! For example Prozac is a trade name, Fluoxetine is a Generic name but they are the same thing. The same applies to Lamictal and Lamotrigine. They are the same thing. Why they would licence one and not the other is a mystery to me. Since they are the same thing, I dont see how they can ban Lamotrigine if it is the active ingredient in Lamictal (Which is openly available)
But the answer to your question is YES, they are the same.