History of England
With Henry VII's accession to the throne in 1485, the Wars of the Roses came to an end, and Tudors would continue to rule England for 118 years. Traditionally, the Battle of Bosworth Field is considered to mark the end of the Middle Ages in England, although Henry did not introduce any new concept of monarchy, and for most of his reign his hold on power was tenuous. He claimed the throne by conquest and God's judgement in battle. Parliament quickly recognized him as king, but the Yorkists were far from defeated. Nonetheless, he married Edward IV's eldest daughter Elizabeth in January 1486, thereby uniting the houses of York and Lancaster.
House of Tudor
As noted above Tewdur or Tudor is derived from the words tud "territory" and rhi "king". Owen Tudor took it as a surname on being knighted. It is doubtful whether the Tudor kings used the name on the throne. Kings and princes were not seen as needing a name, and a " 'Tudor' name for the royal family was hardly known in the sixteenth century. The royal surname was never used in official publications, and hardly in ‘histories’ of various sorts before 1584. ... Monarchs were not anxious to publicize their descent in the paternal line from a Welsh adventurer, stressing instead continuity with the historic English and French royal families. Their subjects did not think of them as ‘Tudors’, or of themselves as ‘Tudor people’". Princes and Princesses would have been known as "of England". The medieval practice of colloquially calling princes after their place birth (e.g. Henry of Bolingbroke for Henry IV or Henry of Monmouth for Henry V) was not followed. Henry VII was likely known as "Henry of Richmond" before his taking of the throne.