Indeed. My passport correctly includes the hyphen in my surname. Air New Zealand doesn't support spaces or hyphens so my surname is written out as both words concatenated (i.e. Onetwo). Qantas doesn't support hyphens but does support spaces so my surname is written out as two words (i.e. One Two).
Thankfully apparently this is common enough that I've had tickets including travel on both airlines (as Qantas cancelled a flight and ticketed me on Air New Zealand instead) traveling internationally work just fine. Even things like the automated customs gates work fine. I suspect under the hood their systems just strips out all non-alpha characters and compares that (i.e. 'onetwo' == 'onetwo').
Online/moible forms can be an issue tho. Spark, the biggest mobile phone carrier in New Zealand, doesn't support hyphens in account names, just to name one silly example.