Trademarks only cover the area and region included in the trademark request. This would keep other companies that do notebooks, folders, and similar supplies from using the name, but not people selling chocolate chip cookies (unless their lawyers manage to get it interpreted over-broadly).

Similarly, if Alex's Pizza got a trademark on their name, it would keep other pizza places in Rolla from calling themselves Alex's, but it would probably not prevent there from being an Alex's Pizza in Idaho or some other distant place. Mead is national enough that this is not a consideration for them, however.

Also, I'm pretty sure that the Mead Brights were released by 2001, which is before the term Bright hit the fan.

These limits are why trademarks can last forever (as long as they're being used), while copyrights can only last... as long as Congress keeps extending them.