She also captioned the photo, 'Birdie's Nest', with two green heart emojis.
"Do we think the babies [sic] name will be Birdie?!" one fan wrote.
Many critics advised Jessica to think twice before handing down the name Birdie to her new baby girl. "Please don’t name the girl Birdie,” one commenter pleaded, while another questioned whether or not the moniker would have "a negative effect on a kid long-term."
However, many also jumped to Jessica's defence. "She can name HER child anything SHE wants," one message read.
Simpson is yet to comment on the baby name controversy, but she's not the first celebrity to choose the name. Actress Busy Philipps chose the same name for her first child, Birdie Leigh, in 2008.