Great observation!
From the documents that I have read from people who were previously enslaved, quite a number of them did not use the same surname of their acknowledge former slave owner. In one of the cases of my own ancestors......My Great, Great, Great Grandmother had at least three different slave owners that I am aware of during her life time and quite possibly a fourth. She took on the surname of her second slave owner. This second slave owner's plantation was were she met and married her husband. They were than sold to her third slave owner to which her husband took on that surname after emancipation. After emancipation, some of the former slaves, on the plantation that she was on last, gave affidavits on her behalf. None of those former slaves' affidavits had the surname of their last slave owner.
Searching for enslaved ancestors using the technique of their surname after emancipation is only one method of researching for them during slavery. I have used this method six times with success in finding my ancestors during slavery. With my other ancestors, I try to gather as much possible information about them from their age, race designation, siblings, parents and even earliest known location to help in my search for them. Most importantly, I also read books, documents or anything that I can discover from history of the local area and state to history and bios of slaveholding as well as non-slaveholding families.
There are no 'one method nor rules' in researching for enslaved ancestors. There is only two rules that I try to apply with each research that I do on my ancestors and that is to: (1) turn every stone; (2) seek out every bit of information that I possibly can from ancestors documents.