From Britain or Brittany
A modern creative spelling of Brittany. It originally referred to people from the region of Brittany in France or the island of Britain. This specific variation gained minor traction in the late 20th century during the peak popularity of the name Brittany.
Less common today
Brittnae isn't in the latest US Top 1000. It last peaked at #7,923 in 1993.
US births per 5-year period, 1990βpresent (SSA data).