1. Before William the conqueror invaded, if you were called Alex, then you would be called Alex. But if someone else shared your name in your area, then you would be called David's son Alex or Alex the carpenter. When William arrived he brought all the surnames over with him like Davidson.
2. The buildings we know as castles were invented by the Normans as the idea was brought with them. Before they were here, we had fortified towns and houses, but when the Normans won the Battle of Hastings, they built towers on top of mounds surrounded by another walled enclosure (called Bailey Towers) and other bigger versions, more like palaces we know today.
3. The Normans introduced French words into the English language because when William I won, he gave all the top jobs to French people. These high ranking nobles still spoke French whilst all the peasants were speaking English. Therefore the commoners started to pick up a word or two and incorporate it into their sentences. This was seen as posh and well-bred. Certain words like chair and parliament were introduced this way.
5. The Normans effectively brought over an economy and lordship. Many Kings and Queens sought to help stimulate their country's wealth. David I of Scotland was exiled and so joined Henry I's court. He was influenced by the Norman culture and when the crown of Scotland was ready for the taking, managed to get it with backing from Henry I. He then brought in the feudal system through English and French knights. With an economy like this, there was space for anyone to rise with increased wealth. Yet it still remained a hierarchy society as invasions strengthened their power.