They told Kidspot they will put the money they save on internet into a savings account for Twifia, hoping she will use it to buy a car when she is old enough to drive.
"The longer I thought about it, the more unique the name became for me, and that was when the thing got its charm," the dad told Kidspot.
"For me, the name Twifia also stands for connection in this context. For an eternal bond," the new mum said.
"There are much worse names. And the more often we say 'Twifia', the heartier the name sounds."
The decision, they say, wasn't easy.
"We want to remain anonymous to those around us because we don't want to justify ourselves," the couple said.
"Because the accusation of having sold our child's name hits us very hard. We are also a little ashamed."
Twifi boss Philippe Fotsch has reportedly said that the couple will get their free WiFi for 18 years even if the company goes bust, as it is "a matter of honour".