After Katie Tomaszewski divorced at the age of 28, she felt ashamed to be alone. So she did what she thought a single person should do: She over-dated, over-worked and over-socialized, inviting friends over for dinner nearly every night because she was afraid of being lonely.

“It was constant socializing and constant distraction,” says Ms. Tomaszewski, now a 36-year-old Pilates instructor in Chicago. “I became desperate and depressed, looking for someone—anyone—to save me from being alone.”

Yes,...