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Last name origins & meanings:

1. English: habitational name from any of various places called Burston, in Buckinghamshire, Norfolk, and Staffordshire, which have different origins. The Buckinghamshire place name is from an Old English personal name Briddel + Old English þorn ‘thorn tree’; the place in Norfolk is named with Old English byrst ‘rough ground’, ‘landslip’ + tūn ‘farmstead’; the Staffordshire place name has the same second element, the first being an Old English personal name Burgwine or Burgwulf.
2. English: possibly from an unrecorded Old English personal name, Burgstān.
3. Jewish (American): Americanized spelling of Burstein (see Bernstein).