Everyone in the current century talks about Goody Addams as if "Goody" was her first name. While in the 17th century, "Goody" was not a name, but a title used for some women like "Mrs." is today, it is probably not a goof. Addams family relatives were known for having quirky and unusual names, including "Anorexia," "Slimey," and of course "Itt." "Goody" as an actual given name would not be implausible.
Sirens are portrayed as half man half fish. They are actually half man half bird.
Fish are not known as good singers.
However, sirens are entirely mythical creatures, so there is no single "correct" way of depicting them. Furthermore, the conflating of sirens with mermaids dates back several centuries, if not millennia.