On the one hand I can understand him putting his name in his hat - all Victorian gentlemen would wear hats, and it's something you'd take off inside and have to collect later. But on the other hand... Would it really have been so difficult not to recognise your own hat? I think you may be right - he put his name in it in case he left it somewhere and it had to be returned ^^ (Unless it's for the hat mender's benefit..?)