That's fully what he had suspected, that he had simply been mistaken for someone else. Thus the reply comes at a surprise, leaving him even more confused.

"I'm sorry, but have we met?"

It was true though that Obi-Wan had used the name, just not on a regular basis. Only for a brief time really. So it wasn't untrue just... depending on your perspective. It's not really a name he answers to though. Not yet anyway.