You don't need to know the make model to know that this is the backlight or the inverter board, or the cable providing power to or from the inverter board.
Cost, however, depends on make/model. But you're looking at anywhere from £50 to £100 for the repair.
It's not a difficult job if you've taken a laptop apart before, but if you haven't then this isn't the best time to start, especially since you'll struggle to diagnose which component is faulty.
If you do take it apart, please heed the high voltage warning label that ought to be near the inverter. You won't enjoy getting a belt off it.