IdahoOrchid,
The cultivar name (such as Phrag. Eric Young 'Rocket Fire', where 'Rocket Fire' is the cultivar or clonal name) refers ONLY to a single plant (and divisions of it), when we're talking about slippers orchids. With Phals and other species that have been cloned and are genetically identical, they also keep the same name, just like divisions.
So, you get to name your own plant, just like you get to name your own dog or cat. There's nothing too special about that. The only reason that cultivar names get well known is if the plant is bred and it's included on the tag of the offspring, or if the plant gets awarded and the name gets published with the award. Obviously, if a plant is awarded, the whole species doesn't get an award, just the single plant... so a name needs to be published for it so that that particular plant can be differentiated from the rest of the plants of that species.
So, what you name your plant is not regulated by AOS or RHS rules, but if you get the plant awarded, then they may not publish the name if it's profane or already taken, etc.
- Matthew Gore