You don’t go far enough in explaining the popularity of Fido as a dog’s name. True, it means faithful. But it is popular because it was the name of Abraham Lincoln’s dog. There is a picture and a story was written about him. Fido was knifed to death about a year after Lincoln died.
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I have to wonder what makes you think Fido wasn’t already a common name for dogs before Lincoln’s Fido. William Makepeace Thackeray’s novel Men’s Wives (1852) featured a dog named Fido, as did the semi-autobiographical novel Our Nig by Harriet E. Wilson (1859).