Terns is not a direct name of Turner. Swan is the direct name of Swann {even though she has two n's in her name} and Sparrow is the direct name of Sparrow.
You know, you shouldn't go around saying that you're unbiased and shit like that then f*cking go say that Will and Elizabet BELONG TOGETHER!
THE F*CK IS THAT!
And swans also migrate and fly to different lands, POSSIBLY symbolising that Elizabeth doesn't just want to stay in her home, maybe she wants to live in different places or just roam.
I doubt the Tern migrates or moves or whatever, but I don't study birds all that much. And the Will Turner, bird watcher coincidence is more a symbolism than that SH*T about Terns.
IT ISN'T EVEN THE REAL F*CKING NAME!
BULLSH*T, F*CKING BULLSH*T!