Step 1: Recall calcination.
Calcination means heating an ore, usually a carbonate, without air, so it turns into the metal oxide and gives off carbon dioxide.
Step 2: Identify calamine.
Calamine is the ore of zinc, and its formula is zinc carbonate $ZnCO_3$.
Step 3: Write the calcination reaction.
On heating, calamine breaks down. \[ ZnCO_3 \xrightarrow{\Delta} ZnO + CO_2 \] So the product X is zinc oxide.
Step 4: Find the common name of ZnO.
The natural mineral form of zinc oxide is called Zincite. So X is Zincite.
Step 5: Rule out the others.
Cuprite is $Cu_2O$, Bauxite is an aluminium ore, and Siderite is $FeCO_3$. None of these is zinc oxide.
Step 6: State the answer.
So the common name of the oxide X is Zincite. \[ \boxed{\text{Zincite}} \]