Jose -
Tbanks for your diligent responses to my previous questions on Portuguese procedures. Here are some further thoughts and questions, based on what you said:

1. Where the child was born - not clear at the moment on that, whether it was a home birth or a maternity clinic/hospital. But if in fact it was at a clinic/hospital - then surely at the time of discharge they would also have to name the child fully on that form you indicate - including first names?

The baby was born in Hospital da Luz in Lisbon.
They might not have registered the baby's name saying they don't know yet what name they will choose.

2. That online site for registration - is that viewable by the public, or is it sealed and only available to view by the registrant?

It is a public and free service run by the Ministry of Justice.
It is part of the Portal of Justice and the Government Portal gov.pt.
It is a public and free access portal that can be consulted via internet.

3. Registering at the Civil Register Bureau - can they send a secretary/assistant to do that, or must one of the parents physically do this registration in person?

Preferably the parents but someone with a power of attorney from the parents can register the newborn baby on the parent's behalf.

As far as what you also said about registering at the appropriate consulate/embassy - UK doesn't issue formal birth certificates from these for "child born abroad of a UK subject". Possibly some other form of registering, but at this point, they still don't have the actual given names to do even that registration - and according to what yuo say they only have 20 days to do it, meaning at the present time...just 15 days and counting. Personally, I think they are waiting until the last moment to do that next step when the media attention has gone down...then send one of their assistants into Lisbon to do that...

Not sure if such media attention will go down before the name is revealed.
AFAIK Eugenie's discharge from the hospital must have been very discreet and received no press cover.
I guess many english reporters and papparazzi might have done the journey.
Yesterday, social networks reported the arrival of Sarah Ferguson to meet her grand-daughter.
Again, no pics of her.
Probably she might have arrived in a private plane and landed in a private aerodrome.