The word LEGO wouldn't exist if not for the company. The wikipedia article actually doesn't say the full story about how the name came to be aka "leg godt (play well)" => LEGO came from a "naming competition" that the founder made and which he ended up winning.
The company would like that the word "Legos" isn't used as it implies that "Legos" are plastic interconnecting bricks of any manufacturer, including the ones that just blatantly copy even the newest LEGO sets.