From 'mantel' (cloak) + 'piece' — originally the smoke-hood 'cloaking' a fireplace before chimneys existed.
A structure of wood, marble, or stone above and around a fireplace; the shelf above a fireplace.
A compound of 'mantel' + 'piece,' where 'mantel' (also 'mantle' in this architectural sense) derives from Old French 'mantel' (cloak, mantle), from Latin 'mantellum' (cloak, covering), possibly from PIE *man- (hand) via the sense of something held or worn about the body, though the PIE connection is uncertain. 'Mantellum' may alternatively derive from a Celtic or pre-Latin source. The architectural sense — the shelf and decorative facing above a fireplace — developed because an early 'mantel' was a hood or covering structure over the hearth to catch smoke, analogous to a cloak thrown over the opening
A 'mantelpiece' is a 'cloak-piece' — the mantel over a fireplace was originally a hood (a cloak-like covering) that caught smoke before chimneys were standard. The same 'mantellum' (cloak) gave us 'mantle' (the Earth's layer 'cloaking' the core), 'mantilla' (a small Spanish cloak/veil), and 'dismantle' (to un-cloak — to strip a fortress of its defenses, as if removing its cloak).