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The family is Lamiaceae. I think maybe what you're looking for though is the species name? The genus is Mentha and usually the species name would be listed right after that, but since yours is a named cultivar those often won't have a species name, it'll just be the genus and the cultivar name. So if you enter it for trading as Mentha 'Silver Himalayan', that tells people exactly what the plant is and that should be all you need.
Are you trading plants/cuttings or seeds? If you're trading the plants or cuttings then you're fine calling it that 'Silver Himalayan', but if you're planning to trade seeds, they may not come true to the parent so I would make sure to mention that 'Silver Himalayan' is the parent but the seeds may look different.