I am gutting my kitchen and turning it into my dining room. I have this built-in lighting structure that spans the length of my kitchen. It is like an upside-down capital T. I am not sure if there is a beam inside of it that is structural or not. If you were to look down on it from the top on either side of the divide, you would essentially see fluorescent lights pointed upward to the ceiling. Dirt and dead bugs collect in this structure, and it is a pain to clean.

Is there a name for this (easier to research if you know what it is called)? What would you do to replace this?