you can name it whatever you want. no formal process except for keeping it in the ' '.
It helps for identification if you have many plants of the same hybrid or species. In the future if your plant gets awarded the clonal name you give it will be used for the AOS records and if you decide to mericlone it and sell the mericlones then this name will be used in addition to the hybrid name.
For example Bc Maikai ‘Mayumi’ AM/AOS is an awarded plant with the clonal name 'Mayumi' given by the grower and it has recieved an Award if Merit (AM) from the American Orchid Society (AOS). And all mericlones are named and sold this way
(hehe name the plant after yourself if you win a AOS award
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