My opinion - previous post - is don't put C64 where is not!
And really - is it important what a name will have computer? Important is that will work without problems... Also - by ROM used.
Power-on message of ROM 911001 is C65, but ROM 910429 has power-on message C64DX... So discussion about name is pretty useless.
I'm in discussion for one reason only - C64-III looks like no C64 fan, but like C64 fanatic.