In my fantasy world, a slave is required to be branded on her upper left breast and also on the right buttock. regardless of her grade. The positions were chosen so that they can be identified easily regardless of various poses they may need to assume. Without the numbers on the buttock, it would be difficult to identify a particular slave when she is crawling on all fours, for example.
Also, a slave is branded on the left breast so her owner (who is likely to be right-handed) may easily grab it for a closer look, especially in a dimly-lit environment like a mining cave, which is one of the more common places where you may expect to find a bunch of naked, virtually indistinguishable slave animals toiling in the dark while covered in filth.
A slave is not a person but just a commodity or resource, so she doesn't need to have a name which implies having a distinctive personality. In that regard, it's only natural for their owners to organize them using numbers, which better be permanently marked on such spots where they can be clearly seen, regardless of various poses they may be required to assume while they are serving their purpose.
On a side note, the position of the brand is also the reason why slaves are supposed to thrust their breasts forwards when they are standing or sitting (which means either kneeling or squatting, as they are forbidden to sit comfortably unless explicitly allowed as a reward) in the presence of their owners.
A slave is, in essence, 'a cunt identified with numbers'. So it's only natural for a slave girl to always expose her genital and her breasts (where her numbers are branded) in full view of any free person near her vicinity.
Slavery is something final and permanent, so it's reasonable to mark slaves using a method which is as permanent and indelible. A slave must be always conscious of the fact that she is nothing but some numbers to her owner, so her whole existence must depend on how well she serves whatever purpose her Master generously assigned to her. Without such a provision, she may develop an illusion that she still retained her own personality independent of her owner. As such, it's better that she should be constantly reminded of her rightful position whenever she looks down upon her chest.
In comparison, an ownership is not as permanent as slavery itself since a slave can always be bought and sold like a used car. As such, a mark of ownership is usually pressed upon the collar she wears instead of being branded upon her skin.
While it's true that slave collars are considered semi-permanent as they are usually welded shut rather than locked with a padlock, they can be still broken by a skilled blacksmith using the right tools. A slave typically serves just a few owners before her usefulness fails to justify her upkeep, such a difficult to change collars isn't normally considered a serious problem.
(Disclaimer: what I wrote above only applies to the common settings I use in my artworks and stories, so it's not meant to be understood as some absolute rule to be followed by any D/s fantasy involving slaves.)