As someone already mentioned, please don’t conflate your part of the West with the West. There’s many Western countries where someone with multiple words in a firstname does not have a first name and a bunch of middle names, or where certain firstnames are formed by compounding several firstnames (the individual words are firstnames in their own right, but the compound name is a distinct name from those which form it).
Fair enough… perhaps anglo-germanic is a better phrase.
I wonder whether it’s significant re. naming conventions that Spain had such a heavy muslim influence in its history (compared with UK, Germany, Holland etc)?
What AK84 has described in detail is the practice in South Asian cultures, where the majority of boys get “Muhammad” in their names and it de facto amounts to a badge saying “This guy is Muslim” more than a personal name. In India and Malaysia they generally don’t bother spelling it out, since it’s a given, and just abbreviate Md. or Mohd.
But in the Arab world, it is applied as an individual personal name and to only some individuals, like any other given name. I’ve seen confusion many times when an Arab is introduced to a Desi.
Desi: Please to meet you, I’m Shahid, what’s your good name?
Arab: My name is Muhammad.
Desi: 
I mean, what’s your… real name?
Arab: Muhammad *is *my real name.