Toilet seats essentially come in two shapes - round and elongated. Toto does make others that would fit - they make one out of painted wood, and heavier units designed for commercial use. I do not know if the ultimate shape is the same.
Any brand would fit, but the curve or color may not match as well. What is standard is the location of the mounting bolts. You could probably use the anchor bolts from Toto to install a different brand.
Personally, I don't use my toilet seat as a storage platform, so the crown doesn't bother me. After a week or so, the curve of the seat isn't a problem, either. It does help to center you and help minimize skid marks that you wouldn't get with a flat seat.
How long have you had it? Have you actually used it yet? I'd give it a trial of at least a few weeks, then decide if you needed to replace it.