Taking to her Instagram Stories, Dani was asked by a fan whether she has a "theme" for the babies' names, the star saying that they have decided what they will call them.
"I think we have decided both names..." she said. "Jarrod always wanted one of the names so that was settled for twin 1.
"However, twin 2 I was struggling as I always wanted a certain name but kept thinking would it work (it's not the most common name), but I'm going to go for it as I think I'd really regret not choosing the name I always loved deep down."
Reflecting on the backlash from some over her decision to name her first child Santiago, Dani noted: "People really have negative opinions on baby names. I had that a lot with Santi, so I'm prepared for that again."
Confirming the twins' sex recently, Dani revealed to fans that she was halfway through her pregnancy, writing on Instagram: "A lot of you have been asking on the gender of our babies and we are so excited to share with you all that we are having identical twin girls.
"Any tips/recommendations I am so open [to]."
Recalling the moment she found out that they will be girls, she added that they were too excited to do a formal reveal: "I'm so glad I got to share the news with you all.
"I'm so gutted though that me and Jarrod didn't do the whole 'pop the balloon' thing or when someone cuts the cake and its pink or blue."
They had the sex written in an envelope, and opened it right after their appointment: "As soon as we got in the car Jarrod was like 'I need to know what it is'. We really should've done [something], but it doesn't matter."
Love Island airs nightly on ITV2, and is available via catch up on ITVX and BritBox.