It's the name of a city in Mexico, but it's also a common surname in Spanish-speaking countries.
However, if you're looking for the meaning behind the name itself, it's a bit more complex.
Monterrey comes from the Spanish words "monte" (mountain) and "rey" (king), which could be interpreted as "King's Mountain" or "Mountain of the King".
So, the literal meaning of Monterrey in English is a combination of the words "mountain" and "king", which can be interpreted as "King's Mountain" or "Mountain of the King".