If you're talking about starting a game using the "start from an older update" option, there's an item in your inventory to change your name just like with the "latest update" option.
If you're talking about an old save of your own, where you've already selected your own name but now want to change it again, you'll need to head to Sal's Market and speak directly to one of the clerks (as opposed to over the counter) to buy the name change item