From Black's Surnames of Scotland…..
FAA, FAW, FALL Three spellings of one name. Faa is or was a common surname among the Border Gypsies (Groome, Gazetteer 1 p 408) and Faw was the spelling in Shetland. Sir David Faw was chaplin of Rosemarkie 1451 (OPS II p 582)
Dr Fae or Falle was principle of Glasgow University in later quarter of 17thC (RPC 3. serxii p522) Wm Fall burgess in Montrose 1672 Robert Faa was alte ballie ofMelrose 1692 (RRM iii p114) Robert Fall or Faa was member of Scots Parliament for Dunbar 1693 and Robert Fau feuaer in Coldstream 1830