There are some names that are historically associated with orphans in Portuguese and Spanish. In Spanish the usual name is Iglesias, which means literally means "churches" (It's also a very common name). They could also say "Bautista" for John the Baptist, de María for Mary, Santos (which just means "Saints", etc). These surnames was given to orphans since most orphanages in Spain were run by Catholic religious orders such as the Franciscans and the Dominicans.

In Portugal, the same sort of thing was going: religious orders were running the orphanages and preferred religious surnames like Trindade (Trinity), Santos (Saints or All-Saints), de Jesus (of Jesus), Pais ("Fathers"), de Deus (of God), Batista (Baptist, for John the Baptist), or Filho (Son). These names were also adopted by people who were very pious or devout, not just by orphans.

However, Spanish- and Portuguese-speaking people usually have two surnames, one from their mother (usually her father's name) and one from their father. An illegitimate child (a "bastard") would just take his or her mother's surnames unless his or her father decided to legitimize or adopt him or her, in which case he or she would take one of his or her father's surnames like a child born in wedlock, or if the child wanted to take advantage of the father's potentially high stature in society he or she may use his father's surname to emphasize his or her filial relationship to him.

In England after the Norman conquest acknowledged bastards were given a name with a Fitz, a Norman French noun meaning "son of", from Latin filius (son). Fitzroy was often given to royal bastards "son of the King". However it wasn't only bastards who could get of Fitz name, nobles of the time usually took the name of the place they ruled, so for instance Roger who ruled Beaumont would be Roger de Beaumont. Nobles who didn't have lands couldn't do this, so they often would use the Fitz name as well, so a knight with no lands named Roger whose fathers name was Gilbert would be Roger FitzGilbert. So while Fitz was used for bastards it wasn't solely a bastard name like in A Song of Ice and Fire.