When you come across a dolphin that is not your partner, Catherine will prompt you to befriend it. Make friends as usual by patting, nudging or whistling to find more information about the creature. When you have two bits of information (you will need to come back on a different day for the second) the dolphin will appear at your boat the next time you return. Use the Ramp and you will have the option to make it your partner. If you have three partners already you will be prompted to get rid of one of them to make room for the new. The next time you return to the boat the rejected partner will visit to seek reinstatement or say goodbye. Once you have given your new partner a name they are ready to be trained or to be used when diving.

Partner	Location
Beluga	In the 'Prince's Room' in the Ruins once unlocked.
Bottlenose Dolphin	At Central Hall in the Ruins (also found during basic training).
Commerson's Dolphin	South west of Marige Atoll (Mo'ia Atoll).
Common Dolphin	At Dolphin Rock near Sunshine Beach.
False Killer Whale	In or near the White Room of the Caves.
Orca (Killer Whale)	In the Ocean's Graveyard/Ship's Rest around the highest wingtip of the crashed plane (once unlocked).
Pacific White-sided Dolphin	Below the Sloping Hallway (Entryway Slope) at E5.
Risso's Dolphin	In the Secret Cave in the Abyss.