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 Ulf mean?
From the Old Norse 'ulfr', meaning 'wolf'. A common standalone name in medieval Scandinavia and the source of the '-ulf' ending in many Norse compound names.