The pope is not unique in taking up a new name when taking office. Monks and nuns also get a new name when joining a monastic order and it’s not a unique Christian tradition either. Buddhist monks also take up new names. In both cases they don’t usually change their legal name so in official documents they will still show up as their original pre-monastic names. I assume this is the case for the Pope too, he is called Leo but I bet on his documents he is still Robert Francis Prevost.