From Britain or Brittany
A modern variation of the name Brittany or a direct reference to the nationality. It ultimately derives from the Latin 'Britannia', referring to the Celtic people of the region. As a given name, it is a rare contemporary coinage rather than a traditional historical name.
Less common today
Brittish isn't in the latest US Top 1000. It last peaked at #5,540 in 2014.
US births per 5-year period, 1990βpresent (SSA data).