Last names in many places evolved from that same need to disambiguate between people though. Attach some marker of connection to a place (common in Finland, e.g. Joensuu meaning "mouth of river"), profession (common in Germany and UK, e.g. Müller, Cooper, meaning mill worker and barrelmaker), lineage (common in Iceland, e.g. Grímsson meaning "son of Grímur"), or some other culturally relevant characteristic.
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.
Having a name with "of Region/city/former kingdom/..." is often their last name. Unless you want to claim that these people do not have a last name.
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.
