There are a number of types of surname, a place name, like woods, Hillman, Forrest, Highmoor or a real place name, like London, derbyshire, Rotherham,
An occupational name, like Cooper; Smith; Grainger, Fletcher; ; Potter
A character or descriptive name, like redhead; Broardhead; Shortman;
A patronymic (named for father) Johnson; Thomson; magnusson;
A matronymic (named after mother, quite rare apart from Scandinavia)
Names developed as the population grew to distinguish one John from another John, hence John the Copper (barrel maker) became John Cooper,
John the blacksmith became john Smith, and every town had a smith or two,
John from the wood became John Wood, whereas John from the dales became john dale,
Thomas's son became Thomson etc.
In England there was little tribal naming but serfs and peasants living and toiling under the protection of a lord may have taken the lords name, and so the servants of Lord Derby may have used derby as their surname.
the anglicising of foreign names is a different subject entirely, the Huguenots and the German sugar bakers anglicised their names to make them more pronouncable in England and also to give themselves protection.