First thing that popped in my mind was Julie, I don't know why.
But tell me more about the character: - Age - Background
What I did for some of my characters was look for popular names in the (approximate) year of birth (on this site in the Popular names section) I look for names used in the region my character (or anchestors) live or came from. Then I look at the meaning of the names, do they fit my character, is the meaning a description of my character or a certain trait my character has. This usually gives me a list with some names (sometimes just a few, other times a longer list) From this list I choose the ones I like best and write them down with the last name.
For other characters I've chosen names from certain regions or with specific meanings. 'Fire' and 'Royal' where a few very important elements I needed to use with some of my characters names [i](I write fantasy so using an unusual names or 'creating' a name using existing words in ancient languages sometimes works great)[i] I looked at the name themes section of this site, and I used the 'meanings' option in the 'search' box.
Most of my characters have more than one name, they are named after family members or I used several names with different meanings that gave the most accurate description of my characters.