The "Girls" alum said the list was made in 2015 and poked fun at Antonoff for suggesting the name Carrot.
"Hey @jackantonoff I just found a potential baby name list we made in 2015. I could definitely keep this private, but then the world wouldn't know that you suggested "Carrot" over and over... Love u!!!" Dunham captioned the list on Sunday.
Other names on the list included Oz, Kelly, Na, Ricki Lee, Jacki, Eddy, Joy, Sara Lee, Zavie, Toni, Camilla, Loretta, Rah, Shogo, and Clare.
Dunham, 32 and Antonoff, 34, a musician and producer, split in January after more than five years of dating.
The split was said to be mutual, with the pair remaining friends afterwards.
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