The baby boy was born on Friday, January 22. The duo, however, are yet to file the baby's birth certificate, reported Aceshowbiz.
"Louis and Briana are yet to file a birth certificate but they've agreed on the name Sydney Rain. It will be rubber-stamped in the next five days," a source said.
"It's not yet known whether the baby boy will take Briana's surname or Tomlinson," added the source.
Given that the One Direction singer is no longer in relationship with Briana, they have to resolve custody of the child. "There's already a lot of talk about who is going to pay what. The family have slightly exaggerated expectations of what Louis should be contributing every month," said the source.
The singer came close to Jungwirth in May last year after he separated from longtime girlfriend Eleanor Calder.
He is reportedly in relationship with "The Originals" actress Danielle Campbell, currently.