Ironic that for all the elite lineage captured here, the one that he ended up stuck with is a very plebeian surname of non-hispanic (Ligurian) origin.

I would like to know more about the conditions under which Spanish family names became "X y Y" rather than "X" or "Y".

Inheriting both surnames is traditional, picking one is nontraditional or foreign. The interesting option is between using a conjunction or not (Paul Davis Thefirst or Paul Davis y Thefirst), which seems mostly a matter of sounding better or, as Wikipedia suggests, disambiguating between first names and surnames (if it precedes the conjunction it is a surname).

No, the surnames are Ruiz and Picasso.

The rest are given names and nobody uses more than two. It was in the baptism record where all the saints of the days used to be added. I have a similar record with a dozen names, but only two given names in the civil record, of which I only use the first.

Visions of Epic Rap Battles of History when you read it spelled out like that: https://youtu.be/WGN5xaQkFk0?si=aKCPFF_yfy6ly8Tb&t=61