According to mate-desktop.org it is MA-TAY:
Where does the name come from?
The name “MATE”, pronounced Ma-Tay, comes from yerba maté, a species of holly native to subtropical South America. Its leaves contain caffeine and are used to make infusions and a beverage called mate.
But I do not care how you pronounce it, just as long as you do not say it is an English word 
Source: http://mate-desktop.com/