I can't fully answer the best way forward on this. But I do know it is BA's responsibility to change any ticket they issue rather than AA, assuming it's a 125 ticket. I have a weird character in one of middle names thanks to my hippy parents, and I just ditched that name altogether but I guess that's not an option here. I would be tempted to let this ticket slide (no, they won't be denied boarding) and just remember to avoid umlauts consistently in all future bookings.

[I am surprised Bremen didn't just change the name, they must get it all the time].