Cetus's own article centres Mira, the variable star whose name means the wonderful. A different, much steadier star in the same monster's outline became famous for a different reason: it was one of the first two stars anyone pointed a radio telescope at, hoping something might be listening back.
Tau Ceti lies about twelve light years from Earth, one of the nearest Sun-like stars in the sky and long considered a promising target in the search for other planetary systems. In 1960, the American astronomer Frank Drake aimed the Green Bank radio telescope at Tau Ceti and at Epsilon Eridani in Project Ozma, the first serious scientific search for signals from another civilisation, monitoring each star for a narrow radio frequency that might carry a deliberate signal. No signal was found, and none has been found since, but the project set the template that later, larger search efforts have followed for decades.
Tau Ceti's appeal was entirely practical rather than mythological: close enough to study in detail, similar enough to the Sun to plausibly host planets, and quiet enough at radio wavelengths that a faint artificial signal might actually stand out against it, criteria that have nothing to do with sea monsters or ancient princesses.
The choice of Tau Ceti over any of Cetus's other stars was an astronomer's judgment call, not a mythographer's.