Hi Ian Hope your search progresses well but if I can offer one piece of advice - forget the Village and any famous people bearing the name. Renwick is a mix of Anglo-Saxon and Old English and probably translates as REN - Roe Deer or Raven and WICK as Farm or Dwelling. Basically DeerFarm or RavenFarm. Having been to the village of Renwick I would guess Raven as it really is a morbid little place. Anyway, it's highly unlikely that there are many (if any) Renwicks connected to the place - it's kind of romantic to think you have a village named after you!. The name has some early roots in Northumberland (previously Northumbria)and the Boarders region although there are early mentions in East Anglia. Unless you have anything positive to go on start looking in and around Hexham/St Johns Lee and Alston for Northumberland and Roxboroughshire in Scotland. There are a lot in Tyne and Wear (Formerly County Northumberland) - try Ryton, Gateshead and Newcastle from the late 1700s early 1800s to date. In the 1700s a lot of Scots moved to tyneside for industrial work whilst conversly people involved in working on the land tended to move into the South of Scotland (land was cheap) so families developed Scottish or English lines quickly. The name is not Celtic (Pehtas, Picts or Scots)so the Scottish Renwicks were basically imigrants however it is possible the name dates back to the 5th century so the first Renwicks could have moved North to Scotland soon after that. That said, the Scots were at war with the Anglos' for some time so my guess would be a couple of hundred years later.
Remember early records are not too reliable as the further back you go fewer could read or write so you could encounter Rennick, Wrenick etc etc.
If you have some names let me know - I may have some info that'll help although I've tended to stick to my direct ancestors.