I know in some latin cultures, the mother's maiden name goes last. In America, we tend to hyphenate the last names, and put the mother's maiden name first.

So, Arturo Renaldo Ramirez(father's) Garza(mother's)
or

Arturo Renaldo Garza-Ramirez

Either way it's plenty acceptable. :) Ask the dad, too! Sometimes dad's like their own surnames to be passed on as the "family name".