Welcome to FT!

I had my names transposed by an Indian travel agent once. To make things worse, he attached my middle initial to the front of my last name (which was first). So, if my name (in the Western name order) was John Q. Smith, he had me as (again, in Western name order) Qsmith John. However, once I told check-in agents to look for me under "John," not under "Smith," and what my first name would look like, I had no trouble boarding any of the seven legs, U.S.-India and within India. They all felt that matching the individual pieces was sufficient even if they were in an unusual order.

Based on that experience, I don't think you have to worry. Check-in agents see thousands of passengers. You will not be the first person they have seen with this sort of problem. Some of them have documents that are far more messed up than this!