But when it comes to her real life relationship with Fun. guitarist Jack Antonoff, the two-time Golden Globe winner says she's found love.
"I know there's some rule that you're not supposed to talk about your boyfriend publicly just because it seems like all starlets under the age of 33 have decided not to do that, but if you're in love with someone great, then I don't understand why you wouldn't tell everybody," Dunham says in the February issue of Interview magazine.
"You don't have to post naked pictures of them on the internet or Tweet pictures of your Christmas celebration, but I feel like, in a way, he's my best advertisement, so I'm like, 'Why would I not tell people who ask?'"
With the second season of Girls under way and Dunham winning two Golden Globes at Sunday's 70th Annual Golden Globe Awards, her star power is quickly rising.
"I've started to get used to people feeling like they already know me when they meet me. I've obviously only experienced it within the past year of my life, but it's really interesting to have so many people who you're not familiar with act familiar with you," she says.
Though her parents are artists Carroll Dunham and Laurie Simmons, success didn't come easy for Dunham – who made her directorial debut with 2010's Tiny Furniture.
"I know that in my family – despite the massive amounts of acceptance – it was thought that in order to be a person who is really contributing something to the world, you had to be generating things creatively. So performing was only really interesting to my parents in the context of things that you create," she says.
"I think I'd aligned the idea of liking [acting] with having a horrible ego or something, and admitting that I liked it or that it was important to me – even to myself – just didn't feel okay."
She continues, "I always had these two things of feeling really respected and connected at home, and going to school and feeling like I just could not get it right. I didn't feel like the other kids got me, but then I was also sort of bored and annoyed by them, so I knew that a large part of it was my problem. I actually had to switch schools because I didn't have friends. I remember my parents saying, 'She is so victimized at her school, so she has to switch.' But I was like, 'I'm switching schools because I'm an a–––.' "