There's a whole Potter Name Etymology website at http://www.theninemuses.net/hp/3.html but it's pretty amateurish (in the deprecatory sense of the term).
The name is celebrated in Cornish history. It originates in a local land unit of Cornwall called a 'barton': the barton of Trelawny, in the parish of Alternun; and another barton called Trelawn or Trelawny in Pelynt parish. Trelaun in turn means 'open town' or 'clean town' in Cornish, according to page 126 of Patronymica Cornu-Britannica, or the Etymology of Cornish Surnames by Richard Stephen Charnock, Ph.Dr., F.S.A., F.R.G.S.; London: Longmans, Green, Reader and Dyer, 1870.
Potter name etymologies
The name is celebrated in Cornish history. It originates in a local land unit of Cornwall called a 'barton': the barton of Trelawny, in the parish of Alternun; and another barton called Trelawn or Trelawny in Pelynt parish. Trelaun in turn means 'open town' or 'clean town' in Cornish, according to page 126 of Patronymica Cornu-Britannica, or the Etymology of Cornish Surnames by Richard Stephen Charnock, Ph.Dr., F.S.A., F.R.G.S.; London: Longmans, Green, Reader and Dyer, 1870.