as a former travel agent I have seen this a number of times - it is the least terrible thing that can happen with a name because it still matches what is in the passport , albeit in the wrong order , I have never yet heard of anyone having any problem with this form of name error after having notified the airline ( bear in mind too , that Japan is used to westerners having forename and surname the other way around from what is the norm in Japan )

(It's embarrassing to admit as a former TA but I did it to myself once on an online booking - because the airlines website used forename/surname where the standard practice I was used to in the GDS is to use surname/forename - I got a lot of ribbing from the airline over it )