Although papaya is classified a fruit, in the realm of Brachos, it is considered a vegetable. This is because the papaya tree displays vegetable-like characteristics. For instance, unlike other trees, papaya trees produce fruit during their first year. It is for this reason papaya is exempt from the laws of Orlah, which only applies to fruit trees. Therefore, reciting a Hoadama is appropriate. (Shulchan Aruch Orach Chaim 203, Kaf Hachayim 213:13, Yechave Daas 4:52). However Rav Belsky thought it best to recite Haetz and Hoadama on a separate fruit and vegetable, and then eat the papaya.
Blessed are You, Hashem our God, King of the universe, Who creates numerous living things with their deficiencies; for all that You have created with which to maintain the life of every being. Blessed is He, the life of the worlds.
Baruch Atah Adonai Eloheinu Melech Haolam, Borei Nefashos Rabos V'chesronan Al Kol Ma Shebarasa L'hachayos Bahem Nefesh Kol Chai, Baruch Chei Haolamim.