There are no specific criteria used to arrive at a name for a zoo animal because zoos are allowed to choose whatever name they would like for their animals; however, most zoos will allow the public to vote on names or will allow the animal's keepers to name the animal. The Woodland Park Zoo had lion cubs in 2014 that they named themselves and allowed visitors to name.
Two of the lion cubs were named "Mandla" and "Gandia" by keepers while the third was named "Tandie" due to popular vote by zoo visitors in a naming contest. A similar approach was taken at the Targona International Zoo where two of three otter cubs were named by the facility and the other otter cub was named by visitors through name suggestions given on the Targona International Zoo Facebook page.
If someone is interested in learning more about how zoos name their baby animals, then the zoo of interest should be contacted to see what their specific procedure is. The only criteria that zoos will follow for naming is choosing names that are not considered offensive in any way and that do not conjure any profane images. Many times, zoos will also use names that have a particular meaning, such as the lion cub with the name of "Tandie." Tandie means "fire" in Scottish.