Depends I guess. Most of the Original Characters I've ever used are just throwaways to fill in the scenes. A name in a paper, a shop owner, things like that. For Potter, I use the following rules:

'English' names. Names that don't stand out.

Henry Baker - good.
Kimberly - not so good.
Violet Shadow Ravenwood - absolutely terrible.

 

When I create a truly fleshed out character (I do this mostly for original fiction, since when I do write fic, there are rarely OCs in it), I generally have at least a first name in mind while I create it. Usually it's something pretty ordinary that "fits" the character's personality. When I choose a surname, which I don't always use in the story since most of the stuff I write doesn't call for it, I think about what I know about my character. Their ethnicity, their family background, etc. Last short story I wrote, for example, was about a character named Cassie Martinez.

For HP, I think it's important again to think about who your character is, and what purpose do they serve in the story. Is he/she English? Scottish? Indian? Are they Muggleborn or wizard raised? Are they important enough to warrant a name with a "tell," like Minerva McGonagall, or are they just background characters, like Susan Bones? If they are, what does their name tell about them? And how can you make it sound canonical without crossing into Raven Shadowynd territory?

Personally, I prefer that OC interaction be kept to minimum unless it's by a fantastic writer. I'm not a fantastic writer, so most OCs I use in fic are the inconspicuous ones.

 

Sometimes I try to make anagrams of meaningful words to the character, or of people on whom the character is based.

 

Once I looked through mythology books for a series of hours, writing down interesting names and occurances for use in my own projects. Then I realized that I probably wasn't the first person to have that idea, and I stopped immediately.

I tend to use short names. For example, I wrote 2000 words about a character named Sean Lewis, and 1500 words about a girl named Ella. I try to go for something unexpected, but it all depends on what kind of tone you want your story to have. If you want it to be humorous, "Bam Hammerstein" might not be as stupid as you think, provided the guy actually carries a hammer--preferably like Roran in the Eragon books.

Anywho, non-descript, random names unrelated to their character traits
are usually the best way to go though.

 

Or you can go the opposite way and use names that are completely and utterly wrong for the character. It works especially well in humour fics because as soon as you see a name like say... Flint Rockford you don't immediately think of a ballet dancer. Works even better if you pick really over the top names.

Terry Pratchett had some good ones like the Carter family - Hope, Prudence, Chastity and Charity... Who don't really follow the paths their names might take. As well as their brothers, Anger, Jealousy, Covetousness, Deviousness and Bestiality Carter - who has been nothing but kind to animals.