Lady Gregory, she of W B Yeats fame, recorded the following passage in her book on Irish folklore (you can read an online version of it here).

…and Eochaid was drowned with his children; and the water spread out into a great lake that has the name of Loch Neach to this day. But Liban that was one of Eochaid’s daughters was not drowned, but she was in her sunny-house under the lake and her little dog with her for a full year, and God protected her from the waters. And one day she said "O Lord, it would be well to be in the shape of a salmon, to be going through the sea the way they do." Then the one half of her took the shape of a salmon and the other half kept the shape of a woman; and she went swimming the sea, and her little dog following her in the shape of an otter and never leaving her or parting from her at all.

– from A Book of Saints and Wonders by Lady Gregory

This is reminiscent of a Catalan fairy story, The Girl-Fish, recorded by Andrew Lang, in which a girl is transformed into a salmon.  Of course there are countless folk stories about people who go to live in the sea, or about mermaids and mermen, supposed by some to have originated from sailors’ sightings of mammals with fish-like characteristics, such as the sea cow.

Then she told him all her story, and how it was under the round hulls of ships she had her dwelling-place, and the waves were the roofing of her house, and the strands its walls. "And it is what I am come for now" she said "to tell you that I will come to meet you on this day twelve-month at Inver Ollorba; and do not fail to meet me there for the sake of all the saints of Dalaradia." And at the year’s end the nets were spread along the coast where she said she would come, and it was in the net of Fergus from Miluic she was taken. And the clerks gave her her choice either to be baptized and go then and there to heaven, or to stay living through another three hundred years and at the end of that time to go to heaven; and the choice she made was to die. Then Comgall baptized her and the name he gave her was Muirgheis, the Birth of the Sea. So she died, and the messengers that came and that carried her to her burying place, were horned deer that were sent by the angels of God.

– from A Book of Saints and Wonders by Lady GregoryJenny Haniver

There are various sites in the British Isles where mermaids and other sea maidens were supposedly brought ashore and baptised/buried.  Although it sounds incredulous, in the sixteenth century there were in fact a fair few mermaid corpses in circulation.  Those same sailors who’d fantasised about manatees were still inventing monsters when they reached the shore.  Sailors would carve and varnish the bodies of dried skates and rays to create freakish figures known colloquially as Jenny Hanivers (read a good Time Magazine article about it here).  These could be presented to superstitious landlubbers as the bodies of sea saints and girls of the deep.  The rewards could come in the form of hard cash, or simply the fun of a well-executed practical joke.