Leonardo da Vinci is another famous example of a last name with two words in it. It's very common in romance languages. Plus, lots of people in the American south just flat out have two first names or two middle names.
Nowadays the meanings of our last names have largely disappeared, so you have countless Coopers who have never touched a barrel in their lives, whose children will be called Cooper also, despite that. I think it's a little sad that so much of what people call us is semantically equivalent to a random UUID with tons of namespace collision. With that in mind, I'd say "da Vinci" is more a last name than most of us have.
Seriously, though, it just feels apropos.
I can understand that in some cultures this might seem weird or antiquated but here in Germany these names are reality. Sometimes people with such names are descendents of royalty and sometimes someones last name "from family-name" is thier last name and happens to historically correspond to one of germany's state names or city names or just a little town.
One a side note: In Germany in 1919-1920 royalty was no longer a legal aspect that changed how laws applied to you[1]. When that happened titles that were reserved for ruling functions (king, grand duke) were removed and all other titles were moved to be part of the persons name (such as prince etc.) and could not be decreed on anyone new. These titles still exist in Germany but are simply naming "conventions" in a formerly royal family.
[1] https://de.wikipedia.org/wiki/Adelsrecht
[edit] In Leonardo's case perhaps not but still i wish to elaborate a litte on the situation here.