Surnames

People in England generally did not have hereditary surnames before the Norman Conquest of 1066.  Many had by-names, descriptive nicknames used to distinguish between very similar family names.  Surnames as we know them today began in Carolingian Europe and came to Britain with the Normans and Flemings after the Norman Conquest.  Most land-owning families had surnames by 1300, everyone else had a surname by about 1500.  Yorkshire, with its Anglo-Scandinavian tradition of using bynames (or epithets) and patronymic surnames, took longer than the south of England to fully adopt fixed surnames and Scotland took even longer.  More Flemings and others bearing existing hereditary surnames arrived in the fourteenth century.  Parish registers were introduced in England on 5th Sept 1538 by Thomas Cromwell, the advisor to King Henry VIII.

Taken from this article by George English on the University of St Andrews Scotland and the Flemish People webpage:

All surnames fall into one or other of four classes (alternative terms in brackets):

1. Local Surnames (Locational, Locative, Toponymic, Territorial, Landed) e.g. Torkington, Crosby, Scott.

2. Surnames of Relationship (Patronymic, Fealtic) e.g. Wilson, Robertson, Macauley.

3. Surnames of Occupation or Office (Occupational, Official, Trade) e.g. Smith, Falconer, Stewart, Corner.

4. Nicknames (Descriptive, To-Names) e.g. Brown, Campbell.

This website from the North East of England lists and gives origins for many of the more well-known Borders (southern Scotland, northern England) surnames and includes several Rox2 surnames. 

Surname distribution in the UK: https://named.publicprofiler.org

Britain and Ireland SNP and Surname Tracker: http://scaledinnovation.com/gg/biMapper.html

See this more detailed subpage for notes on Corner-Cornay surname history.