Seven manuscripts and two fragments compiled in the 800s AD [after Offa's Dyke] compose what came to be called "The Anglo-Saxon Chronicles". It was written in the vernacular at the monasteries instead of being written in Latin. An ecclesiastical calender was used beginning with the year 1 AD, reading, "Octavian reigned for fifty-six years, and in the forty-second year of his reign, Christ was born." It ends in the year 1154 AD with, "King Stephen was dead this year..." Thus for more than one thousand years, the Saxon recorded their calendar. A lot of names were recorded during this time!
It appears that the Saxon's dominate method of listing names [name calling] was just to give the name! "Severus received the kingdom..", "Bratian recieved the kingdom", "Cerdic and Cynric killed a British king named Natanlaod...", "Hengest and Horsa fought Vortieger the king", and many, many other. Occasionally, a qualifier was used such as "Vortigern the king", and "Theodosius the Younger". Many of the religious leaders were identified as "Archbishop Mellitus", and "Higbald, bishop of Lindisfarne...". Thus it would seem that a religious or social position of standing was recognized. Otherwise, just call them by name.
So the Welsh would tell who their father's, father was. The Normans would tell where they came from. The Saxon would call them by name.
The quotes are taken from a wonderful reference titled: "The Anglo-Saxon Chronicles, The Authentic Voices of England, From The Time of Julius Caesar To The Coronation of Henry II", translated and collated by Anne Savage. It contains a world of additional pictures and items that give a broad picture of the Anglo-Saxons during this period.