When best mate's great aunt registered the birth of her child (she subsequently married as a spinster) she named the father with identical details to those of her brother
We assume she had already given her own surname and then had to invent a father on the spot.
Who you lie to depends on who knows you. GGGgranny gave true father's name to registrar, when she registered little Edmund's birth. Vicar knew perfectly well Louisa wasn't married, so Edmund grew up as a Skillings, not an Edwards.
New Swindon sounds like a growing place, where you could say what you liked, with little fear of being found out.
Did the child live to get married themselves? Or does anyone have the mother's death certificate?