Branding

[Jessica]

Creating a permanent marking in a human or animal by heating a metal object, often [molded] to form the shape of the [owners] initials, and pressed hard into the receipents body.
This was common among farmers who branded their cattle to identify them as belonging to them. This can also be found in extreme BDSM and [sadomasochistic] scenarios, where the dominant partner brands the submissive partner as his or her own.

[Tina]

The action of marking with a branding iron.

[Kai]

To burn the flesh with a hot iron, either as a marker (for criminals, slaves etc.) or to cauterise a wound.

[Lizzy Liz]

The process in which a mark, usually a symbol or ornamental pattern, is burned into the skin of a living person or animal.