What if I decide my "name" is the first billion digits of PI? Are you going to add that to the list of names that you need to support? No?
In economics, people talk about the problem of 'sorting and labeling' and how that is an unconscious reaction (which does unfortunately lead to bias) but it helps immensely in the overall productivity of an entire system.
When people expect you to design special systems which increases the overall entropy, I wonder if they realize that you too incur a cost for creating that system. I say this as someone whose name is constantly butchered during my dealings with American entities, and I am not generally asking them to modify their system to accommodate my name so it remains unaffected. Thankfully, in most cases, I actually have a choice of whether I should continue having dealings with such entities. (I don't know what happens in cases where you don't, like, say the DMV).
When you store it as a single string, which order will you choose? Will you have delimiters between them? Would they still be in effect when the person's name has more than 2 parts? If you are ever in a situation where you need to sort by name, will you do it by first or last name? What if there is a need for the other option to the one you chose? Can you reasonably guarantee that you can identify family members if you ever need to? When the customer tells their name over the phone, will it slow down your customer service people if you display the entire name in a way which they are not usually familiar with?
2. Sort by the whole thing
3. No you can't guarantee identifying family members any more than with a first name last name system. If you need that it should be an additional part of the system. Presumably for the 90% of people who does have a typical first name, last name combo you can still identify family members in the same way.
4. Just introduce free text search for this field if you need to find people.
But suppose you are working at a place where people are keen on getting 'smart with the data', your replies do increase the entropy if only to the extent that 'we have this idiot programmer who thinks he is too smart to use first and last names as we have always done and is breaking all our reporting systems and is causing hell for our customer service agents'.
:-)
That is the wrong way to handle this. You don't have to support everything in the list. If your product is only for people in America you can expect them to have a name written in latin letters. You can ask them for a surname and a given name, and they will be able to fill it in, but may be slightly annoyed. You should allow apostrophes and accented letters, but it's really not hard these days with UTF-8. ASCII is too limited.
As you support more countries you will need to support more kinds of names.
At least in the states, legal regulations on names vary from place to place. In the state of Texas, if you're a lawyer, you are legally required to tell people this, most commonly done by adding the Esq abbreviation for Esquire at the end of your name. I have a friend who's official name (of course I've obfuscated this) is "Dr. Firstname b. Lastname PhD, Esq.".
How many latin letters are there anyway, 26? 600? I read the latter number in an essay on what typesetters used to keep. Is ' an English letter, as in O'Malley?