First, some background about names. Names are labels we use to convey the essence of something. The first place we find the procedure of giving a name is when Adam names the animals, and then names Chava. The difference between this naming of animals and the naming of people is that animal names describe the species but not the individual, whereas people names describe only the individual.
The Talmud tells us that the name given to a person can affect his character, and we are therefore careful to give our children names that will affect them positively. The Talmud also explains the verse in Proverbs "The remembrance of a tzaddik (righteous person) is a blessing, and the name of the wicked should rot" to mean that one should not name a child after a wicked person. Another aspect of the significance of names was told to me by Rabbi Moshe Shapiro, that when a child is named after someone, the child "continues in the footsteps" of the first person, in order to complete their original task.
Now, on to your question. After investigating this subject, here is what my research has yielded: Ashkenazim (Jews of Eastern European descent) fairly often name their children after animals, while Sephardim (mainly descended from Spain and Arab countries) seem to do so less frequently. One phenomenon that I encountered in my research is that when Rabbi Yosef Karo (a noted Sephardic halachic authority) lists the spelling of names for the purpose of writing a Get (bill of divorce), none of the names are "animal names" — yet when the Rema (a noted Ashkenazic authority) lists names for the same purpose, he includes many names of animals. I asked Rabbi Chaim Pinchas Scheinberg: "Why would one group choose names of animals and another would not?" He told me that really neither group is naming their offspring for animals since we are careful about "contaminating" our children with the tumah (impure spiritual effect) of non-Kosher animals.
So why do people seemingly name children after animals? The answer is that when they name their children they are not naming them after the animals per se, but are recalling the qualities of the great people of early generations who are exemplified by those positive animal traits. When someone is named "Aryeh" (which means “lion” in Hebrew, and is often Leo or Leonard in English) the trait of our ancestor Yehuda is being evoked, a lion-like and royal "king of the beasts." With the name of "Zev" (“wolf” in Hebrew) we are recalling our ancestor Binyamin, whose character was wolf-like — "a mighty and fearless warrior". The animals are mere symbols of very human qualities.
"Yehuda ben Teima said: Be as fearless as a leopard, as light as an eagle, as fast as a deer and as powerful as a lion, to do the will of your Father in Heaven."
