So how should you start looking for a seat cover?
For sure, it is very rare that you would have to buy an entire new set of toilet just because of the seat cover.
Unless of course, the model is really really old.
But there's a good chance that someone has a compatible seat cover you could use!
The first stop is to find out the brand and if you can, the model number of the toilet. You can then try to find the local distributor of that brand. Send them a picture, front and side view. This should help them identify the model.