The name of the salt used to remove permanent hardness of water is :

Sodium carbonate decahydrate ($Na_2CO_3 \cdot 10H_2O$), commonly known as washing soda, is used in industries and households to remove the permanent hardness of water.

• Option (a) is incorrect because Sodium hydrogen carbonate ($NaHCO_3$), or baking soda, is used as an antacid, in baking, and in fire extinguishers, but not for removing water hardness.
• Option (b) is incorrect because Sodium chloride ($NaCl$) is common salt, used primarily as a food additive and a raw material for manufacturing other chemicals.
• Option (d) is incorrect because Calcium sulphate hemihydrate ($CaSO_4 \cdot \frac{1}{2} H_2O$), or Plaster of Paris, is used for plastering fractured bones and making decorative items.