From Britain or Land of the Britons
Britiany is a modern phonetic variant of Brittany. It originally denoted a person from the region of Bretagne in northwest France, which was settled by Britons fleeing the Anglo-Saxon invasions of England.
Less common today
Britiany isn't in the latest US Top 1000. It last peaked at #4,216 in 1990.
US births per 5-year period, 1990βpresent (SSA data).