I want to write a story that takes place on another planet and I'm wondering if my characters should have last names or not. I know that here on earth people have not always had last names. If I remember right last names didn't become common in the west until the late medieval early renassiance period.
If you want last names you could always take the idea of using the job, or location as a last name. Play with that idea, you could also make up last names based on when the characters are born or so on. If not they don't really need last names not unless there's a reason for them.
If you feel your characters need another name, but aren't sure if they should be last names, you can always try titles. Titles were a form of "last names" before there was such a thing. If you want to use last names though go ahead, just because the story is on another planet doesn't mean that they can't have a similar custom.
Your story, your decision. One thing you might consider, though, is the population of your world. Not necessary the world in a literal sense, but the "world" of people for members of a community. If you have a dozen population centers, a population center with millions of people n eeds a more complex naming system than an isolated community of a couple hundred with little to no contact with other centers.
I have planned that on one planet the population is about 40,000 with a majority of the population living in the capital city. There are other places in this world where people live but none are nearly as populated at the capital city. There isn't an economic system on this planet so there is little trade. The main way of sharing and communication on this planet is through technology. Then I have plans for another nearby planet that has a higher population of about 30 million with most of the population living in a city called New Engaland City. There is also the capital city where most of the political activity takes place. There are also other major cities most on the coast of the ocean. There is plenty of trade on this planet and also lots of sharing and communication through technology. Should I make it where on the less populated planet people don't have last names and on the more populated planet people do have last names.
First name-personal, usually after something in the nature or a fabled individual. Middle name-lineage, mostly maiden name or first names within the family, but later act the same as first names, and last name - occupation, place of origin, title or "son of" a forefather. I think last names show, even if it is something like "Joshua, the marksman", show some form of bureaucracy that show advancement. It is your choice to present how advanced the civilization is.
In the past (before medieval ages) there were last names of some sort, usually stating the lineage of the person eg.John Stuartsson (John, son of Stuart) or John Stuart(John son of Stuart). They go as far back as ancient Greece(maybe more) so you can use something of that sort.
