The name "Patricia" is derived from the Latin word "Pater" which literally means "Father."
The word "Patrician" actually means "noble."
"Noble" means, as provided by dictionary.com, "of an admirably high quality; notably superior; excellent."
From Wikipedia: In modern English, the word patrician is generally used to denote a member of the upper class, often with connotations of inherited wealth, elitism, and a sense of noblesse oblige.
I myself believe that the name "Patricia" must mean she cares for her family, since the Latin word "Pater," means father, in which a father is considered a solid provider for his family. She cares and provides for her family, as a father would.