I wanted to find a way of raising this question within the limited strictures of SE so please bear with me on the explanation.
When we think of personal names, we immediately think of given-names and surnames, often using the more informal and less-correct terms forename and last-name. In almost all places where names are stored - in genealogy and in other areas such as government databases - there is an attempt to formalise names and categorise their elements. Hence, the parochial Western knowledge of worldwide names often gets enshrined in data storage and it can adversely affect people from other cultures.
So, for Western type names, we obviously need to account for possible multiple middle names. Then we find there may be academic titles (e.g. Dr. or Prof.), honorific prefixes (e.g. the honourable, or his holiness), honorific titles (e.g. Sir, Lord, Dame, Lady), or post-nominal letters (e.g. VC, OBE, PhD), generational titles (e.g. .Jr, Sr, I, II, III, etc).
As we move out of the English-speaking world, we find cultures with multiple surnames. The surname category itself has to include patronymic or matronymic names which are a different type of inherited name element. In Far Eastern cultures, there is a generational-name concept that we don't have in the West. There is also a general class of name element called a 'name particle', analogous to a grammatical particle. This includes all those small joining words such as: “von”, “van”, “der”, “de [la]”, “d′”, “the”, “[son] of”, “mc”, “mac", "Ó", "Ní", "Nic", "Mhic", "Bean", "Ui", "y", etc.
Even if the storage supports extended-Latin or non-Latin alphabets, we find different rules for capitalisation (sometimes it is not the first letter of an element, and sometimes it is more than one letter), and sorting (e.g. sorting on the first, last, or other name element).
The Native American cultures effectively have unstructured names that defy all attempts at formalisation, so this is a problem even within the US. A name like Running Deer has no surname concept. If our representation of names is to include pseudonyms, stage names, and other alternatives - any of which could be a simple mononym - then we have to abandon any formalisation.
In my opinion, we're chasing a non-existent formalisation, and all such approaches are doomed. So, my question boils down to: What are the essential properties of a name that we need to record and to distinguish, over and above a simple sequence of name elements? If a product (or data format) supports alternative names for a person, each of which is a simple sequence of elements, then do we really need to know about surnames any other element types?
You might be prepared to answer about inheritance of names and helping the end-user. Well, even ignoring the unstructured Native American example, above, we find multiple rules for inheritance. Some cultures have matrilineal inheritance as opposed to patrilineal. In the Irish culture (and others) the surname is not simply tacked on and there are different rules for men and women of different generations.
It seems for every rule, there will always be valid cases that don't fit.