All of the elephants were born in the orphanage; thirteen of whom were born last year, while rest of the two in 2010.
Nihal Senaratne, Director at the Pinnawela elephant orphanage, said that the naming of each baby elephant was determined by an astrologer.
"An astrologer looked at the time of birth of each elephant. He then decided on the first letter of each baby's name according to its horoscope," Senaratne said.
The names given were: Singithi, Ahinsa, Themiya, Wanamali, Trinky, Elvina, Nandi, Mangala, Annuththara, Jeevaka, Kadol, Isira, Bimuthi, Aithi and Gagana.
Foreign and local visitors who were visiting the orphanage were also asked to give names. The foreigners named two of the babies.
The orphanage, about 80 kilometres east of Colombo, is a major tourist attraction where large crowds gather to watch the elephant bath.
The elephants are herded to the nearby river for the daily bath. Pinnawela opened in 1975, currently houses 83 elephants, most of whom were abandoned or separated from their herds when they were babies. Many have also been born at the orphanage.