The FlashForward star and his wife Maria Dolores Dieguez welcomed their daughter earlier this month but WENN reports that they still haven't settled on a name.
"[We had a] baby girl, [we're] looking for names, so any suggestions would be welcome," Fiennes said.
"It's Baby Love right now, but I've got to get her passport together because we're going back home soon, so I think by the weekend we'll have something."
Fiennes added that the birth had been "amazing" and revealed that Dieguez had chosen not to take any pain medication during labour.
"In the [birthing] pool, no drugs, no nothing," he said. "Amazing midwife, amazing obstetrician, and hypno-birthing, and she was just amazing, breathing... The last ten minutes went a bit primal, I have to say, but it was a beautiful, beautiful moment."
> Joseph Fiennes: 'Fatherhood is beautiful'