Offset Wants Daughter to Have His Last Name

Offset's got a few requests in his ongoing paternity case with one of his baby mamas ... and chief among them -- he wants their 4-year-old daughter to have his last name.

The Migos rapper filed legal docs, obtained by TMZ, in his case out of Fulton County, Georgia requesting that his daughter, Kalea, take Offset's last name. Offset's gov't name is Kiari Cephus. In docs, Offset says he's the biological father to Kalea, who was born in 2015.

The rapper's baby mama, Nicole Marie Algarin, named the girl Kalea Marie Algarin, but Offset's requesting the name be changed to Kalea Marie Algarin Cephus. There's more ... Offset is asking for joint legal and physical custody of their daughter.

As we first reported ... Nicole, who goes by the stage name Shya L'amour, filed docs last October asking for more child support from the rapper. Offset claims he is already paying support and says both parties should be financially responsible for their daughter.