Hygieia was often depicted as a young woman feeding a large snake that was wrapped around her body or drinking from a jar that she carried.
The two statues of Fames flanking the Papal Crest on the Attic are symbol of future recognition of the Pope that restored the fountain for the people utility.
In Roman mythology fame is personification of public acclaim and usually was portraited with a trumpet in her hand. When she has two trumpets, one served to announce fabrications, the other one truths.
Triton is a Greek god, the messenger of the sea. He is the son of Neptune, god of the sea, and Amphitrite, whose herald he is. He is usually represented as a merman, having the upper body of a human and the tail of a fish. Like his father, he carried a trident.
However, Triton's special attribute was a twisted conch shell, on which he blew like a trumpet to calm or raise the waves. Its sound was so terrible, that when loudly blown, it put the giants to flight, who imagined it to be the roar of a mighty wild beast.
Statue of Hygieia, I century AD, Ermitage Museum, Russia