So it should be "Broetli", then...?
I even do it with my name most of the times. A Chinese official that sees Ø in my passport won't understand why I write 'OE', and might even start questioning if it is the same name, but 'O' never fails.
Airlines can read the gibberish in the bottom of my passport and see that the transliteration is actually 'OE', but most places don't have a scanner for that.