Garay / Garaizar
They are both Basque surnames from the Basque country in Northern Spain & Southern France.
Garay is common in Vizcaya / Encartaciones area (Sopuerta, Gladames) , there is a hamlet called Garay. I know, my ancestors had this surname too and I am from there.
Lots of Basques left for America from Columbus' days to the days after the Spanish civil war, forced into exile by the dictatorship.
It means something like "height", "place above the hill" or something like that.