From Brittany or Great Britain
A modern creative spelling of Brittany, referring to the region in northwest France settled by Britons. The name originally denoted someone from the province of Bretagne or the island of Britain.
Less common today
Brittanni isn't in the latest US Top 1000. It last peaked at #5,036 in 1990.
US births per 5-year period, 1990βpresent (SSA data).