Most of my brass has "Remington" stamped on the head.
The main reason is that I buy brass in decently large quantities, generally 1000 or 2000 at a time, and I insist that it all be of the same lot number. My supplier can generally meet those requirements with Remington brass.
However, I recently loaded some .22-250 for a fellow and he insisted on Winchester brass. I managed to get 500 pieces of the same lot number, and the brass was a mess! I have never seen fresh factory brass arrive in such poor shape.