Instructions on how to register a new orchid hybrid are here:
Orchids / RHS Gardening
Ray already noted some requirements.
Anyone can name a cultivar but it usually doesn't happen until it awarded or cloned, and sometimes not even when it is cloned. But any plant that is cloned or even just divided should get a cultivar name, otherwise somewhere down the line there could be much confusion. Feel free to give your plants cultivar names, but try to make them something unique that no one else would choose. 'Pink' is bad, 'Zyxqu Pink' is much better. There are restrictions on cultivar names too, but they are so often ignored it hardly matters.