It's called a rack.
A hob is a shelf at the side or back of a fireplace.
The shelf over a fireplace is called a mantle.
mantle. Mantel Mantelpiece Mantelshelf
A shelf on top of a fireplace is commonly referred to as a mantel. It is used for decorative purposes and can hold various items such as picture frames, candles, or seasonal decorations.
A hob.
chimney
A mantle.
A shelf above a fireplace or something that covers or conceals
hob
One can find shelves over the fireplace from Home Depot. One can go online to check with the shelf they want, then order it online or pick it up from store.
The corner of a fireplace is called an Inglenook!
The shelf in a hatch back is a partial shelf. A parcel is a package.