Typically, I can get a first name for most main and recurring supporting characters. I've used theme naming in two works. One was a fanfic continuing from where the anime left off, so I used the naming convention from that; the other, which used alcohol types and brands, was all my own. Most of the time, I try to avoid theme naming unless the character's parents are the type to engage in that.
I once took a course on creative writing, a short one offered by the City of Ottawa and taught by a magazine editor. One of the things she mentioned is that characters are influenced by their parents, including the names. There's two ways to approach the idea. The first is to figure out who the parents are and then how they would come up with the character's name. The other is start with the character and then work backwards.
I tend to use the second method the most. A good example is from /Subject 13 - Nasty herself. I began with just her and her nickname. From there, I expanded her name so that Nasty worked as a nickname, and came up with Natasha. I then gave her a last name, Giuliano, which implied her heritage, Italian. Working from there, I figured out her mother's name, Maria, but working out what an Italian Catholic would name a girl. It doesn't explain why Maria named her daughter Natasha, a name that derives from Russian. I've worked out an explanation, but it won't be revealed until Issue 55 or so.
Another factor to consider is nicknames. Again, I'll point at Nasty, who is referred by her nickname even in the narrative. Meanwhile, over at the Lethal Ladies, Allison is the only one to get a nickname, Allie. The other Ladies have names that aren't easily turned into nicknames, either because of length (Rose), lack of a good alternative (Amber), or refusal to answer to one (Elena). Meanwhile, in Subject 13, nicknames abound. Nasty (short for Natasha and reflective of her personality), Rennie (short for Renata), Jess and Jessie (short for Jessica), Rusty (from her hair colour), Stormie (reflective of her personality), and Skeet (long, untold story). The difference between the two stories may come from the difference in cast size; Subject 13 has a far larger cast.
Last names, or family names, are also important to a character's identity. Even though many characters are easily referred to by just one name, for example, Buffy, they mostly have a last name or family name, with those without being the exception and a key part of the character's background. Sometimes, I'll be limited in the range of names. A Russian character won't have an Irish surname, and a fantasy character might not have a family name, just a trade or home village. Looking at the Threefold, I wanted Miriam's last name to reflect her heritage, thus becoming Miriam Goldman. Astrid, meanwhile, was named after her mother's favourite children's writer and thus doesn't really have a tie to her last name. Since the Threefold's story is set in a modern setting, this isn't a problem. In a fantasy setting, the mix-and-match style won't work. Rufus, that most excellent priest, never received a last name. My last PC for D&D Encounters was called Varendae of Shadowdale; her home village was, indeed, Shadowdale.
With last names, I don't always have an idea of what I want. I tend to look for names that work well with the character's given name. Closing credits of movies are a good place to look, especially outside the cast. Few people notice the names unless they stand out, like Killmaster. For nationalities that are under-represented in Hollywood, there are other options. Eastern European and Nordic names can be found on NHL rosters. Anime credits are good for Japanese names. Hong Kong cinema provides Chinese names. When in doubt, pick a year divisible by four and look up the Olympic team for the country of your choice for that year.
There are a few other little tips and tricks I keep in mind. Never use two names that sound similar, unless that's part of the plot. It avoids confusion between the two. Avoid names that start with the same letter, unless the sound is completely different between the two. I ran into the issue with Lethal Ladies with Amber and Allison. If one had been Amy instead, the confusion might not have occurred. Not everyone has a fancy name. I know more Daves than I have any right to in real life. Minor characters can break these guidelines; Steve the barista and Steve the gunman aren't going to cause issues if they appear in different chapters.
In short, names are important. They give the reader a way to remember the character, helping to make that blob of a personality a definition.