From Britain or from the land of the Britons
Britnay is a modern phonetic spelling variant of Brittany. It originally referred to the region of Bretagne in northwest France, which was settled by Britons fleeing the Anglo-Saxon invasions of England.
Less common today
Britnay isn't in the latest US Top 1000. It last peaked at #7,439 in 1992.
US births per 5-year period, 1990βpresent (SSA data).