Brand is the Danish, Dutch, German and Swedish word for "blaze/fire", "burning" and "burned".
Brand is the second champion to be based around a fire theme, the first being Annie.
Brand's ability, Sear has a similar in-game animation to Annie's auto-attack.
Brand's auto-attacks also have the same animation as Morgana's auto-attacks, though changed in color from purple to orange.
Considering Lokfar's similarities to stereotypical vikings and Norsemen of the past (Olaf), Brand may have been inspired by the fire giant Surtr of Norse mythology. His appearance follows a common description of the character (blackened skin with lava crackling underneath), and Brand claims he is destined to renew the world by burning it, which is Surtr's role in Ragnarök.
Brand could also have been inspired by Ignus of Planescape: Torment, due to both of them being mages basked in flames, burning their enemies, and having lost their humanity to become what they are now.
Pyroclasm is most likely a reference to Vaan's Quickening of the same name in Final Fantasy XII.
The body that Brand is currently occupying once belonged to Kegan Rodhe, a seafaring marauder.
This concept of possession may be in reference to human branding, a process in which a mark is seared into the skin of a living person, with the intention that the resulting scar will make the mark permanent. This was used as a method to impose ownership over an oppressed person.