Like is a button which allows Facebook users to express their approval of photographs, links and status updates of other users.
Lior Adler and his wife Vardit, who live near Israeli capital Tel Aviv, said they were looking for a name that would be "modern and innovative", and then decided to keep the name "Like", the Daily Telegraph reported.
"In our opinion it's the modern equivalent of the name Ahava [Love]," Adler said.
"It's just my way of saying to my fantastic daughter, 'Love'," he was quoted as saying by Israeli newspaper Maariv.
According to the Haaretz newspaper, the most popular names for girls in Israel currently are Noa, Maya and Tamar.
Like's parents have a fondness for unusual names. One of their daughters is called Pie -- after the English food -- and the other is called Vash -- Hebrew for Honey.
Adler said the reaction to the name had been mixed. "When I posted her picture and name on Facebook I got 40 'likes'," he said.
"Considering that I have only a little more than 100 friends on the network that's a lot. "But not everyone was keen on the name and some friends "simply didn't believe it", he said." I believe there will be people who will lift a eyebrow ... but it is my girl and that's what's fun about it."