I agree. My great-aunt was stillborn, and she was listed as "Infant" on her death certificate. When she was buried, she had been given the name of Barbra, and that's what is on her grave marker. I listed her name as Barbra, but I posted a copy of the death certificate that I have and explained the circumstances of the names.
My great-grandfather is another situation. He was less than a month old when the census taker came around. On that census, he was listed as "Rufus". I don't know if he was actually named that at first, or if the census taker pushed for a name for the census. In any case, a short time later, he had been renamed "Jacob" which he used the rest of his life. Again, I used Jacob as his name, but I explained in the biography section what had happened.