Thinking of these things in opposing terms which exclude one an other isn’t exactly helpful.

Take a moment to think about this: Which authority in the UK would have a law about Christian names? The government, or a church? And would having multiple names together for a person be illegal (and subject to punishment) or would it be extralegal or unlawful and simply not recognized within the jurisdiction concerned (UK civil/governmental law or some Christian denominational church doctrine?).

Law is law, sure, but which law by which authority and in what context? Multiple can exist simultaneously. Civil law, church law, etc. Not all things are neatly congruent, agree with one another, etc. Please take the time to avoid conflating such things.

This is making a big deal out of very little. A Spanish civil name has restrictions that a Catholic baptismal name may not. They need not be the same as one another with respect to the same individual, one does not invalidate the other, etc. In a civil framework requiring a civil name, that is what would be used.