Eclipse's father has a house in the northwestern part of the city. After the events at the LCCC, Aster brings Eclipse's lifeless body back to her father. She can then be found lying in bed. Completion of the sidequest rewards a Shiny Charm.
The player can trade an Electirizer for an Elekid in the house to the right of the Gym. The Elekid has one of these Egg Moves in its moveset: Cross Chop or Ice Punch.
After the Battle of Agate story segment, find a woman named Murmina hiding in a storage room outside Calcenon City, connected to Route 4. After battling her, solve the Calcenon Gym's floor tile puzzle to access a secret room. Inside, give Murmina the Family Picture found at the Belrose Manor to receive a Torchic Egg in return. Torchic doesn't have any Egg Move in its moveset.
Calcenon City likely derives its name from chalcedony, a common oxide mineral, or less likely calcite, another common carbonate mineral.
According to Florinia, Calcenon City was originally the residential sector of Labradorra City before it was purchased by Silph Co. and rebranded after the collapse of Reborn City.