What is the name of the special candle of Hanukkah?

It's called a Hanukiyah or Chanukiyah. Many people call it a menorah, but menorah just means lamp.

Answer 2:

The above is completely mistaken. The Word "Hanukkiah," while acceptable, is a recent Israeli invention and is unknown to many Jews worldwide. And using "menorah" to refer to a mere lamp is also recent.

The classical Halakhah (Jewish law) sources, and Jews worldwide, have always used the Word "menorah" to refer to the Hanukkah candle-holder (or oil-wick holder). Originally "menorah" referred to the candelabra of the Holy Temple and the Tabernacle (Exodus ch.25).