I've been told that many surnames came from a combination of parent/child names, and that in other cases a person's trade or location was responsible for the surname.
However, the history of our surname seems to imply that it was chosen at some point as part of a dedication to a cause.
This led me to wonder how somebody could choose their surname, rather than having it assigned by cultural norms.
This can be very complex depending on the region of the world and even at regional level, comes with costumes, cultural traditins and I suppose hazard.
True that across Europe is not strange to find surnames based on occupations, Smith in Englisg speaking countries, Herrero o Ferrero or a variant which is the counter part in Spanish and Portuguese and old Castillian or in Germany if you like F1 Schumacher (Shoe maker) . BUT in some of these places you also find the formula "son of....". Example, in Spanish speaking countries Fernandez, Alvarez or Hernandez are very popular surnames, they originates as Son of Fernando, Son of Alvaro or Son of Hernando respectively, so most ending in dez or ez point to the "son of..." formula. Similar thing in Nordic countries, Odinsen would be son of Odin etc.
You do not necessarily choose your name but it just happens. Let me explain, let's say England 14th century where in the market place a young boy makes a mischief, "hey boy, come here, I know you, you are William, the son of the Blacksmith" (or the Tanner's son, or fit in your own preference) and it sticks. Or let's say a local priest or friar enters your name in a church birth registry once you are born and baptized. "John of the Butcher" or similar and it's easy to see how it will end up in John Butcher.
Before I forget geographic locations are also quite popular pretty much following the same formula. William of Ayr, Thomas of Bruge, etc.
Hope it helps while other explanations flow in.