In José Manuel, Manuel would be the middle name, just like in English. It's not a "two-words-long first name". Sometimes first and middle names are coupled like a whole, like it's usual for José Manuel. Also for José-something or Juan-something in general. Other times, the middle name is never used, like in Nicolás Antonio, being the Antonio part extra annoying, because the SS personnel, for some reason, insists in calling me that when it's my turn.