"I haven't gone by the name of Obi-Wan since, oh...before you were born."

I took that as meaning on a regular basis. Padme called him Obi-Wan just before she died after having the twins. He went on to live on Tatooine almost immediately after. This is about nitpicky as you can get. The twins birth and his move to Tatooine is about the time he stopped being called Obi-Wan on reg basis. How else could this have possibly been done to line up with what you thought it meant? Of all things to criticize, I think this is nothing. So telling Luke he hasn't gone by that name since, oh before you were born. Is not inaccurate. Some people wanna take everything extremely literally, when people don't necessarily talk that way in real life either.