As far as I'm aware someone can call themselves whatever they like so long as it isn't done with intent to defraud. I'm sure a lot of us have people who swapped the order of their names, took on step-parent names, swapped between mother and father surnames if illegitimate, married several times... some people wanted to curry favour with a wealthy relative, others to remarry without divorcing, others running from the law... I don't think there was any actual impediment to him calling himself Joe Bloggs instead of John Smith. People weren't tracked in the same way we are now so I don't know how many people would have cared what he called himself. He was up front about being a widower... provided he was being honest, obviously.
I have one ancestor who was, like yours, dropped by aliens onto the 1881 census where he married shortly afterwards. It eventually turned out his birth was registered under his married mother's surname (her husband having died two years previously...) and was on his first census under her remarried surname before taking her maiden name for the rest of his life. Nothing dodgy there, but it certainly made it complicated to find!