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In Game of Thrones S08E04 The Last of the Starks, Gendry is
legitimized by Daenerys & pronounced as Gendry Baratheon, the Lord of Storms End.
When Gendry finds Arya, he tells him that his earlier name was Gendry Rivers.
and now it's Gendry Baratheon & proposes marriage to her.
As far as I know, Gendry was born in Kings Landing.
Bastards of Kings Landing are named Waters. Bastards of Riverrun are named Rivers & Bastards of Stormlands are called Storm.
So, where exactly was Gendry born? Was this a plot error from D&D?