Basic information

Name: Search pet or baby naming books and websites. Some sites even have the most popular names for particular decades and locations. Also search for lists of foreign/exotic names, or simply peruse the phone book.
Sexual Identity: Male, female, hermaphrodite, homosexual (gay or lesbian), bisexual, eunuch, spayed, sexless, transgender or shape shifter.
Age: fetus, infant, toddler, child, preteen, teen, young adult, adult, middle age, late middle age, old age (geriatric - which is actually the medical science), ancient, immortal or revanant.
Species: Relevant for science fiction and fantasy stories.
Race, Religion, Ethnicity, Nationality, Type or Subgroup: Anything that is pertinent to the character's appearance, beliefs, loyalties, or identity. There are exhaustive possibilities to explore.
External Links
Babynames.com
Name generator
Fantasy name generators