Just booked flight myself and the exact same thing happened to me, so it definitely seems to be a problem with the site as I triple checked all my details, but once I clicked on submit it switched the names.
I was using chrome web browser, maybe that has something to do with it?
I also could not select my seat using Chrome, had to login with Internet Explorer and then it was fine.
Anyway I'm going to try forward this to the web development team for Qatar as I think it is something that needs to be fixed.
Perhaps a Qatar Representative on this forum can point me in the right direction?
Regards,
Wes