Buildings, shops and inns frequently used painted signs to distinguish them. This could be a king's oak, a gilted lamb etc. It is reasonable to believe that names of pharmacies developed from medieval names of buildings. The Swan is linked in Christian symbolism to the death agony of Christ. The swan is such a brave creature that death does not frighten it.
Man also has nothing to fear.
The swan gives man strength to endure painful illness and courage to face death with hope. The lion was used as a pharmacy name because of this Christian symbolism. The art of medicine and the preparation of medicines was considered the oldest and most nobel art - a royal art. The elephant cannot be linked directly to Christian symbolism. It functions more like a kind of commercial trademark and was meant to give the layman an impression of the mysticism surrounded by medicines, spices and herbs originating from far-off countries.