“Santa Claus” comes from the Dutch/Belgian holiday figure “Saint Nicholas”/”Sinterklaas” who has pretty much the same role here (*). Meanwhile, the Saint Nick figure in turn originated from a Turkish saint (the Patron Saint of Children) as far as I’m aware, yes.
Also, Sinterklaas is pretty well known in some versions to be acompanied by a former African slave he freed (**), and who willingly helps him in turn out of gratitude. See it however you will, but to me it seems like Santa and Sinterklaas would fully support BLM.
(*)Key differences being using a white stallion instead of reindeers and a sleigh, and not living in the North Pole. Also, you’re supposed to keep your shoe out with a carrot or something else for the horse instead of a sock with cookies.
(**)In other versions of the story it’s either a white helper who is simply always covered in chimney soot; or outright Krampus.