It's pretty much industry standard that the name in the PNR/ticket should match that on the passport. What you are normally known as is irrelevant.
So Horatius William Smith will not be accepted for travel as Billy Smith, but Horatius Smith might be ok.
Problems arise with names such as Jose Luis Miguel Antonio Camacho de Goncalves, whose name will have to be truncated as many systems are character limited. Some of the GDSs will accept up to 64 characters but ticketing systems and DCSs typically less. The system will truncate by lopping off the extra characters on the end, a human operator may make a more pragmatic decision and enter the above as Camacho de G/Jose Luis M A Mr
To some degree the problem is alleviated as many international destinations require APIS information to be sent through and the SSR DOCP element which is transmitted to the airline should be sent exactly as per the passport.
Oriental and Arabic names are a problem too. Let's not even go there!