TMZ obtained a copy of the birth certificate ... which lists her full name as ... Bodhi Jameson Rein Brown. The little girl was born last Thursday at Cedars-Sinai in Bev Hills.
We don't know for sure why Bobby and Alicia Etheredge picked the name Bodhi -- but in Buddhism the word refers to Buddha's enlightenment. More recently ... it was the name of Patrick Swayze's badass character.
Last year, Megan Fox and Brian Austin Green also named their son Bodhi.