My Farmer has always been Bobbi, just like in Hogwarts Legacy and Ark and My Time at Portia and whatever other game gives you the option to choose. They often look pretty similar in-game too, depending on my mood at character creation.
However.
In Stardew Valley specifically, I do find myself accumulating various titles during gameplay which I could and should change my name to, including:
Dread Pirate Queen Bobbi Cooper
That farmer again
The Perpetually Lazy Fisherwoman
Emily's Town Mannequin
Miss Fall in the Skull Cavern Flying Serpent Tasty Knees Farmer Pinup Calendar
She Forgot Again
Return Sceptre abuse overachievement, 3 years running
- and -
Emily's wife