A local social commerce website, FabFind, heard about the dilemma and came up with an idea to have people vote for a name. More than 1,300 names have already been submitted to Facebook.
Aria and Melania are currently battling for the lead.
"I like them both, but I think now we've kind of started thinking more about Melania. We started sort of lobbying for that name more a little bit," said Rommy Alpinelli.
The parents have selected Lauren as their daughter's middle name.
The person who submits the winning name will win more than $600,000 in deals from the FabFind website, and expectant mother Rommy will get $40,000 in deals.