middle or last names?

I was wondering if anyone can tell me if "del Refugio" or"de Jesus" etc are last names or middle names. For eg. Maria del Refugio Pena Lopez and Jose del Refugio Jimenez. I'm not sure then that I have Jose's mother's last name. The same thing with de Jesus. I have a Jose de Jesus Hernandez and a Maria de Jesus Hernandez. In this case, am I missing both their mothers' last names? or are they related?

Lavaniya