Will it be an old money name? A family tradition? A one-of-a-kind Hollywood moniker? We may not have the answers yet, but we're sure the name the parents decide on will become influential, to say the least.
As we wait for more hints from Sofia herself (who has kept particularly tight-lipped on the topic), we did find out the one name soon-to-be dad grandad Lionel Richie does NOT want...
"You can't call her Lionella," Lionel Richie joked with E! News in January. "You know what? I'm gonna leave that to the parents. I'm just gonna be that loving Pop-Pop that comes in the door and spoils the child."
Whilst the Richie clan are keeping out of the baby name guessing space, many fans are throwing out their own predictions, which range from the obvious to the creative.
One popular prediction is that the married couple will incorporate Elliot's mother's name, Samantha, into their daughter's full name - either as her first or middle name. Samantha Berg passed away shortly after Elliott was born after suffering complications in childbirth.
Another popular suggestion from fans predicts the couple will go with a unique albeit obvious choice - Sofia's maiden name Richie.
Other fans have suggested classic cames like Elizabeth, Charlotte and Isabelle.
Eloise, Matilda and Georgia have also been popular predictions.
At this stage neither Elliot nor Sofia have revealed any hints or comments on their preferred name, so it looks like we'll have to wait a bit longer to find out - let's just hope they don't take the Kardashian route and keep the name under wraps!