A birth certificate obtained by TMZ shows that the couple have named their baby daughter Bodhi Jameson Rein Brown, along with giving details of her birth at 8:24pm on 9 July 2015 in Los Angeles' Cedars Sinai hospital.
Bodhi is a Buddhist concept that can be translated to mean "awakened" or "enlightened". The baby girl is the couple's second child – they already have five-year-old son Cassius – and Bobby's sixth.
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Bobby Brown and Alicia Etheredge have named their baby daughter Bodhi
The new arrival is a rare bit of good news for the family, who have been under increasing strain after Bobbi Kristina – Bobby's daughter with the late Whitney Houston – was discovered unconscious in her bathtub at the end of January.
The 22-year-old has been in hospice care in Atlanta for three weeks, and on Wednesday fresh concerns were sparked about her condition when a hearse was seen reversing into a white tent that has been erected outside the back door of the hospice.
Bobbi Kristina's family did not comment on her health on Wednesday, while the hospice didn't explain why the tent had been set up outside.
Bobbi Kristina Brown has been in a hospice for three weeks
Several family members and friends paid a visit to Bobbi Kristina's bedside after the hearse had arrived including her aunt Pat Houston, her uncle Tommy Brown and Whitney Houston's former bodyguard Ray Watson.
Bobbi Kristina's family have been at her bedside daily, however it was recently suggested that only close family members would be able to visit after someone tried to sell photos from her bedside.
"The hospice, based on their decision with the fiduciary, has decided that only the guardians and the caregivers are allowed," a source told People.