Despite their names never being spoken in the film, they are taken from the book Bambi's Children by Felix Salten, the sequel to the original story Bambi: A Life in the Woods. They are also used when they are featured in the comic book "Four Panel #30" under the story name "Bambi's Children", the same name as the book.
Geno is Bambi and Faline's older son. He was born a couple of minutes before Gurri. He has orange eyes like Bambi did as a fawn. He has 12 spots, 6 on each side. He looks similar to Bambi when he was a fawn. He will grow up to be the next Great Prince of the Forest.
Gurri is Bambi and Faline's younger daughter. She has blue eyes, like her mother, and has a lot of similarities to Faline as a fawn. She has 12 spots, 6 on each side. When she grows up, she will be a princess.