If you have a cattle ranch in much of the West, unless you buy it with a brand already owned, you have to create one for your cattle. Brands might be some part of an owner's name or an imaginary symbol. What it cannot be is what some other rancher has.
Actually you can use a symbol already used. There aren't a lot that aren't, but it will be placed in a different place on the calf. Yep, you brand calves in that country. If that calf is sold, for breeding stock elsewhere, there will be a new brand added.
In the West, I have eaten in cafes where there are branding irons and brands in wood all along the walls. It basically tells you who has been there as well as might still be there. Unfortunately when I was recently at the Empire Ranch in southwestern Arizona, I saw the brands on the post in front of the ranch buildings but did not photograph them. How unthinking was that? But there were several that the ranch could legally use. The contracts to attain these rights are historically preserved as they matter.
Brand inspectors make sure brands are accurate, registered and hence that the cattle are being sold by the proper owner. Rustling still happens; so there is a reason for a brand. They are not common however in western Oregon, nor are they required legally-- yet anyway.
Branding can be done the old fashioned way with a fire, an iron with the proper shape to the design on its end, heat it up, calf is roped, neck and one leg generally and the iron (may take more than one) is laid on its side just long enough to make the mark permanent but not so long as to harm the animal. (Yes it hurts, of course).
There are also electric branding irons, no fire required, and these days you can do it with chemicals or freeze branding but there are as many potential problems with that as the rest.
Basically get a work crew including the home front who prepare a big spread of food, wranglers to get the cattle into the pen, ropers who are good at roping necks and one back leg, and most importantly an experienced cowboy who knows how long to lay down the iron, and where it has to be put, and there aren't a lot of improvements over that method in open range country where a tattoo in the ear isn't going to make separating the stock that easy.
There is a reason I am writing this. It's because they say branding matters to a writer also. Of course, it's not laid on your butt, but it has to be established and recognizable. It is where this is heading (to be continued).
