Jose - do you know what the legal requirements are in Portugal for a child born in Portugal with non-Portuguese parents? Which is the case with this child presently. So...must the birth be registered with a state or local office? Must the name of the child be fully shown on that birth certificate when issued? How many days are legally allowed from the time of birth until the application for a birth certificate is submitted?

Parents have 20 days to regist their new-born baby.

There are 3 possibilities.
1. If the baby is born in a Hospital/Maternity, most have Nascer Cidadão (Born Citizen) Counter where the parents can register the baby, before the mother is discharged.
2. Online: Via the portal Registar Nascimento (Birth Register), where they can also apply for the Identity Card.
3. In person: At a Civil Register Bureau.

In case of foreign parents, the child should be register at the national consulate of the parents (namely the mother's, place of birth and residence, if they have different nationalities).
Parents should present their passports or ID cards.

The child can have 2 names and up to 4 family names.
Nowadays one can mix freely the family names and even choose a family name from one recognized ancestor, but until a few years the rule was first the mother's family name and the father's at the end (contrary to the spanish way).
So, theoretically, the baby could be named Elisabeth Eugenie Ferguson Mounbatten-Windsor Brooksbank 😁😁😁