Originally Posted by
Often1
OP - As you have not provided the name of the air carrier, nor the routing, nobody here can provide you a definitive answer. Please do that.
However, as a general proposition, it is a non-issue and occurs all the time by reason of passenger name entry error, computer glitch and sometimes culture, e.g., what is referred to in the booking template as "surname" is the family name which goes first in some cultures.
For that reason, this is generally not a problem either for the air carrier or for border authorities in the case of international travel.
Nonetheless, please post the name of the carrier and route and you will then get the definitive answer you seek.
This wasn't in relation to a specific booking but in general, since I make many bookings, have made such a mixup in the past, and was wondering how fanatically should I be in verifying this each time. Glad to know it's not a big deal.