I've checked Ingrid H. Tague's Dead Pets: Satire and Sentiment in British Elegies and Epitaphs for Animals and John. D. Blaisdell's A Most Convenient Relationship: The Rise of the Cat as a Valued Companion Animal already.
Christian religious names on animals were forbidden under the authority of the Church, as they were offensive to Christianity, but the spread of the Renaissance thought and the departure from the teachings of the Church began to show such labels, to my humble understanding