I have no surname. Glenn Alexander is two given names. I have no surname because I don't want one. My current birth certificate has a dash in the surname field. This stuffs around the government's computer systems no end.
The reason that I have no surname is that they are irrelevant and unnecessary in modern society. Surnames and the way they are passed through male progeny is a throwback to the time when women and children were considered the properties of their father/husband. ie: a male was always the property of his father as denoted by his having that name and a female was the property of her father until married in which the name change signified that she was then the property of her husband. I neither wish to be the property of my father or to own my children. Besides, I know who my immediate family is and that's our business and no-one else's.
It has the further advantage that I use my two names interchangeably, so if there is another Glenn in the room, people can avoid confusion by addressing me as Alex. Though I generally prefer Glenn.
Any children I produce (an unlikely prospect at this stage in my life - never managed to find a woman I wanted to co-parent with) will have two given names, one chosen by their mother and one chosen by myself. They will be able to use either or both as suits them at any particular time.
My name format does play havoc with some badly-conceived government databases that demand a surname though, which is always fun.* I was quite well known (in a "so you're that guy" sense) in the Illawarra Health system a decade back as Glenn A. Onlyname, though Medicare has upgraded their systems since then. I imagine if the government or a big corporation wanted to collate all the information they have on me, it will take longer and with more human intervention to do so than they might like. Sucks to be them. And I won't go into the multiple isolated online identities I maintain (for perfectly non-criminal reasons).
*I did read a book once with a character named "Hen4ry" (the 4 is silent). The character changed his name in order to screw with databases that refuse to accept a number in a name field.
A rose by any other name, still gives me hay-fever - not Shakespeare, though he probably would have liked it.
Tracing back my male lineage, if I did have a surname, it would be Roberts. That is a pretty boring and common name anyway. It is likely a contraction of Robertson, which is itself derived from "Robert's son"*. Now back several hundred years ago (not that long really), no-one had such things, then the king of the land sent out an edict that everyone should choose one. Many people chose based on their occupation, hence the names like Smith, Thatcher, Taylor, Farrier (look it up) and so on. Some chose a name based on their location. Then we have names like Roberts(on). What did this guy actually do? Was his sole role in life being the son of someone else? It does make me wonder if my nominal ancestor was the 11th century equivalent of a 30 year-old guy living in his parents' spare room playing X-box and watching anime porn all day.
* Actually there is even odds that my nominal ancestor was the servant of someone called Robert (Robert's property). Which is a good deal more respectable, but probably not something to brag about.
As for my actual names, they are bog-common Anglo names:
Glenn comes from the Celtic and means "Of/from the valley" (note the double 'n' - spelt with one 'n' it actually means "Is a valley" - and my butt is not that big!).
Alexander comes in from ancient Macedonia (a place which has little geographic similarity to modern Macedonia, irrespective of what their tourist board likes to pretend) and means "Defender of the People" (it can also mean "One who assists" which in my present job is probably quite appropriate).
So my full name could mean "Defender of the valley (people)" which is cool, though totally coincidental - parents seldom take such things into account when choosing names, at least not back when I was born anyway. Alexander is an old family name, and mum says she chose Glenn simply because she liked it.
In my several years working in China, I also picked up a number of other names (please excuse - and correct if you know - my pinyin: I think I have forgotten more Chinese than I ever learned, if that is at all possible!):
GeLan - derived from my first name phonetically and translating to "blue sword" which I guess fits the "Defender of the Valley" motif.
WeiShaGu - a meaning-based translation of my Anglo name, which I prefer.