She is usually shown with a bushel of grain.
Usually a portion of the yield from their crops.
The symbol of Demeter is a handful of harvested wheat
There may be a real person with the name Demeter living today. Usually however the name refers to a ancient Greek goddess.
Persephone spent time with her mother, Demeter, the goddess of agriculture. She was also often accompanied by Hades, the god of the Underworld, who abducted her and became her husband.
At one time she aided Demeter in her search for Persephone, when Hecate found her she stayed in the Underworld with her as her companion.
Demeter, being a harvest goddess, is often depicted carrying grains and/or or a cornucopia. She does not always have these, however.
The "horn" you may be mistaking for the Cornucopia, horn of plenty.Demeter is goddess of the harvest of food from the Earth.
Demeter is a goddess of fertility, grain, and agriculture. She is pictured as a mature motherly figure. Although she is the goddess who taught mankind about agriculture, she is also the goddess responsible for creating winter and a mystery religious cult. Demeter is usually accompanied by her daughter Persephone.
There was no "god of Demeter", Demeter was a Greek goddess.
Demeter
Demeter was not married. Demeter had two consorts in Karmanor and Iasion.
Persephone, Despoina, Eubuleus, Arion, Plutus, Philomelus, Iacchus, Acheron, Hecate (Orphic)