Starting out on a new novel or short story is exciting for me, with that sense of promise of interesting events and discoveries about characters. The first character, usually the mover of the story, appears well developed and named. I may not know this character well, but I can already see a form and personality. And, most important for this discussion, I don't have to work at choosing a name. Finding names for other characters is much harder.
Characters are not all the same, and their names shouldn't be either. I keep a list of characters as they appear and are named, to avoid basic pitfalls. First, I don't want all or many of the names beginning with the same letter. I did this in one mss and it lent a certain poetic quality to the story--that annoying dum de dum de dum de dum. Keeping a list of names prevent me from ending up with a list of characters like this: Paul, Pam, Priscilla, Peter. Second, the names shouldn't be too similar. It's confusing, for example, to read about Sandy talking to Randy about Mandy.
Third, the names of characters should reflect the culture of the story as well as the real world. If the story I'm working on, for instance, is set in South Philadelphia, or Boston's North End, the reader should encounter a lot of Italian names at least for the background characters, such as the man running the corner convenience store or bakery. If the story is set in parts of central Canada, the reader will expect one or more eastern European surnames.
Historical novels pose other challenges. During the 1940s girls were given what we now regard as common names--Ann, Carol, Catherine, Deborah, Linda. Today the names are more exotic--Olivia, Ryan, Shayla, Taylor. If your story is set in the 1700s, many of the names will be biblical--Ezekial, Jeremiah, Sarah (also a perennial favorite, along with Elizabeth).
Fourth, if you have inadvertently chosen the surname of a famous historical person, change it. If you have not inadvertently chosen that name, take a look at the character and ask yourself if your character reflects that person in a responsible way. Books live on after us, and whatever we think we're experimenting with can turn out to be the joke that falls flat at the dinner party. If you want to offer a commentary on a particular public figure, write an essay.
I once used the name Muir for a character intentionally because I have met a number of people named Muir and I felt the character was the kind of person who could have followed in the extended family lines of John Muir. I reread each passage in which the character appeared in order to be certain I had not insulted anyone with that name. In the end I kept the character's name. I also once inadvertently named a character after a famous baseball manager and when I realized that, I changed it. (This is what comes from not following sports closely, but hearing it only as background noise.) The character could perform his role in the story with any number of surnames.
Fifth, no matter what name I choose, if it looks at all familiar, and sometimes even if it doesn't, I check it in a phone book or on line. I also check the names with a google search. Someone somewhere is liable to have a name some writer invented for a novel, and I recognize that I can't guard against every eventuality, but it is important to make a sincere effort to avoid using the name of a real person.
Last, once you have settled on a character's name, live with it. You cannot change this in the middle of the story, or when you're revising for the last time. That is not the time to decide you've always liked the name Marylynne better than Eloise. Writers choose names because each one seems to fit the character, and to change the name means changing the personality of that character after it's already established. If you really want to do that, it's time to start writing another story, with a different character carrying your new favorite name.