In Wales most people only began to adopt hereditary surnames under the Tudors and even in the 19th century some men were still taking their father's Christian name as their surname.
In the Scottish Highlands that custom was abandoned in the 18th century, but the clan system resulted in large numbers of people with the same surname.
This was done by a descriptive addition, known as a by-name, referring to some striking personal quality (Robert le Gros), or occupation (Alfred the Steward), or father's name (Roger Fitz Ralph), or place of origin (John the Dane), or place of residence (Alstan of Boscome).
There was no consistency in this and for centuries afterwards the same person might appear in different records with a different appellation.
The dominance of the Smiths is not surprising, if we consider that every village in the Middle Ages would need a blacksmith.
Saint's names and Biblical names appear, such as Adam and Thomas.
By the Middle Ages one would scarcely know from personal names that the English were descended from Angles and Saxons at all.
This is from the polyptyque (survey) of St-Germain-des-Prs (810), which is wonderfully detailed, giving names and family relationships.
Now and then it might be necessary to distinguish one person from others of the same name.