Another term for 'ring' is 'nasc', though it's usually used in a more abstract manner these days.
Tolkien borrowed the word 'nasc' with some modifications into the Black Speech as the word for 'ring' ('nazg'), hence 'nazgûl' = 'ring-wraith'.
Is the word order required here? I.e. would 'Tugann sé di fáinne' be correct, as both 'He gives her a ring' and 'He gives a ring to her' are in English?