From Brittany or Great Britain
Brittnei is a modern creative spelling of Brittany. It refers to the region of Bretagne in France, which was settled by Britons, or more broadly to the island of Great Britain.
Less common today
Brittnei isn't in the latest US Top 1000. It last peaked at #5,269 in 1990.
US births per 5-year period, 1990βpresent (SSA data).