Not just you! It makes me really furious. It seems both lazy and ignorant. After all, Santa just means saint, and that doesn’t really make sense by itself. As you say, Santa Claus is acceptable.
I’m not worried about Santa Claus and Father Christmas being two separate figures. Like so much of Christmas, it’s an amalgamation of Christian and pagan.
He’s still Father Christmas in our family, but of course the grandchildren hear Santa all the time at school and in the media. When my elder son was three, forty-odd years ago, he encountered the song “When Santa got stuck up the chimney” at playgroup. He had never heard of Santa.
As DoraMarr says, I fear we are fighting a losing battle!