It is called a "snuffer". This term is often misunderstood and misused. Many people think snuffers were used for putting candles out. Actually, their purpose was simply to trim the wick, although the candle was sometimes extinguished by accident.
Snuffers are more often made to resemble scissors. This style of snuffer was used when the candle was protected from drafts by a tall glass tube such as the hurricane shade.