Hi, 
Following a recent thread about Ribeira Seca, Ribeira Grande, I am writing to ask for your help with abandoned children´s records and how we can infer information from the Godparents. 
To find the origin of my mother´s family name Vieira, I traced her paternal grandfather's ancestors, all of whom from Ribeira Seca for centuries, until I reached Paulina Vieira who married Domingos Teixeira (son of Domingos Frois and Maria Gaspar) on September 18, 1688:
Marriage Godparents:
Captain Major Pedro da Ponte Bicudo Raposo and his son Anacleto de Sampaio and his sister Angela de Sampaio (Joao Moniz Carneiro's wife).
Although Paulina Vieira was abandoned at birth, I believe that I have found her baptism record because no other Paulina was born in Ribeira Seca in the previous 30 years and only one Paulina was born a couple of years later, but she'd be only 14 or 15 at the time of the marriage, so I strongly believe that this is the correct baptism record:
Her Godparents are Domingos da Silva Sousa & Maria Gomes (widowed...). 
Here are my questions:
(1) Could her baptism Godparents be her actual parents? They do not show up in her marriage record, though.
(2) Should I search for more information on he marriage Godparents?
(3) Her husband was baptised at home by a priest other than the priest of his parish:
I cannot find his the marriage record of his parents, Domingos Frois and Maria Gaspar. I have only found a marriage between a Domingos Frois and a Maria Travassos on Abril 2, 1657, but I do not believe that they are the same people. 
Should I search records from nearby parishes as well?
Vieira is a common name, especially in Ribeira Seca, so I know that my work is cut out for me, but I would still like to try and find the origin of my family name, and by that I mean the family from mainland Portugal that introduced this family name to Ribeir Seca. So, here is my last question:
(4) Would an abandoned child just adopt a random family name? What were the customary naming practices for abandoned children. I'd expect her to have the family name Camara or Espírito Santo, not Vieira.
Sorry for all the questions, and thanks in advance for your help. 
Best regards,
Carlos