What does Brand mean?
From the Old Norse 'brandr', which meant both 'firebrand' (a burning piece of wood) and, by extension, 'sword blade'. The fire sense is the original one; the name is sometimes glossed 'sword' for the derived meaning.
What does Fafnir mean?
Old Norse Fafnir, the dwarf who turned into a dragon guarding a cursed hoard in the Volsung legend. Flag: this is the NAME OF a mythological dragon, not a common word meaning 'dragon'; its own etymology is not securely established, so it qualifies by being a famous dragon-bearer rather than by literal translation.