One of my favorite places on the Internet is the Social Security name database, which allows you to track American naming conventions all the way back to 1880—a year in which top names for infants included Alfred and Herman for boys and Fannie, Pearl, Lena (!) and Edith (!!) for girls.
Many of the names that were popular in 1880 have already been revived, or seem ripe for immediate picking. I can easily imagine walking into a day-care center and meeting a band of well-dressed toddlers named Lulu, Blanche, Ora, Otto, Milton and Mack. I'm also quite pleased by the hipster-Puritan feel of names like Dovie, Ambrose and Judge. However, due to current events, there is only one genre of baby name that matters today, and that is the K-name.
K-names become more popular as the decades roll by. The mid-twentieth century brings names like Kaye and Karen for girls and Kermit and Kelvin for boys, and by the 1980s, K-names occupy a significant amount of real estate on the "most popular" list—Kristin's up there, as is Karla, Kristina, Karen, Kendra, Kara and the assorted varietals of Katherine and Kristen. Also present: Kris, Kendall, Kimberly and Khloe.
What to name an 1880's Kardashian, though? Probably not Kathryn or Katie—I see a strong Kanye veto on those two. Kitty, Kittie, Kattie, or Kizzie are all relatively attractive options, but my money stays on King, a nineteenth-century name that's recently become popular again, and is currently #256 on the list of names for boys.
But of course we must look to the future and not to the past. Due to other current events, my actual top pick for Baby Kardashian's name is Magna Carter. Emma's, naturally, is Khoire.