Let's be clear, there is no bureaucratic concept of a "middle" name in Britain either.

I'll go back to the statement that I disagree with and fix it:
"I'm a foreigner living in Spain and there is no concept of middle name here"
So, for the sake of all the young Spanish Izán Alfonsos and Scheherazade Almudenas (who, naturally, just use their first names), this should be corrected to:
"and there is no concept of a third, fourth, fifth, etc. name here"
If you have two "middle names" (i.e. Second and Third names) and want to become Spanish, you either need to compound those names (as in Japan) or ditch one of them.