What does Kane mean?
The 'battle/warrior' sense comes from the Irish Ó Catháin, from 'cath' (battle). Flagged: Kane has several unrelated origins - Hawaiian 'man' (and a deity), a weakly attested Welsh 'beautiful', and Japanese readings - so only the Irish line carries the warrior meaning.
What does Leannan mean?
From the Irish and Scottish Gaelic leannan (leannán) 'lover, sweetheart, darling', a diminutive of leann 'affection, love'. Familiar from the folklore figure leannan sidhe, the fairy lover.