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.
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.