If River Song can concentrate on a dress size and this is her second regeneration, why can’t the Doctor concentrate on becoming a ginger?
Woman Time Lords can control the way they will look when they regenerate, while male Time Lords cannot. This was established in Classic Who, when Romana regenerated.
Also, the Doctor wanting to be Ginger is not about the hair color. In Gallifrey, the only ones to have red hair were the people called Heroes which were beings who were time-sentient (meaning they could see all of the time at the same time). So I doubt they will ever make him ginger.
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