The inside of the opening that the stove sits in is referred to as the chamber, There are two options when it comes to the walls of the chamber, Lining the walls with a heat resistant fireboard gives a neat, clean and smooth finish. the boards can be left white or painted afterwards using any water based emulsion.
For people wanting a more rustic look, occasionally the original brickwork can be cleaned and repointed, I say occasionally because the brickwork was never intended to be seen and poor quality bricks were used, also due to staining from soot it’s usually more cosmetically pleasing to board over the old stained and chipped bricks. Although some chambers are in surprisingly good condition. Keeping the original brickwork is just a case of opening up the chamber to reveal the condition of the walls and deciding which option would work best.
For people who are really stuck on having brickwork, There is now the option to have brick board panels that are slithers of real brick laid on to a fireboard and fixed over the old brickwork. However some manufacturers of these boards make panels that look completely fake, I use a company that only cuts the two faces from a real brick, then hand points the mortar joints afterwards which gives them a more natural look. (see images below)