A herbary is a herb garden, and the word also carries an older sense close to herbarium: a collection of preserved plants for study. Both readings are useful and both are pleasantly antique.
Herbs sit at the intersection of several healthy markets: cooking, gardening, traditional medicine, and botanical research. The growing and using of them has a large, engaged hobbyist audience and a commercial trade in seeds, plants, dried material, and instruction.
The name fits a herb nursery, a growing and reference resource, a botanical education project, a community garden organisation, or a herbal medicine information site. On the .org, the educational, community garden, and botanical collection readings are strongest.
Seven letters, three syllables, no hyphen, and a word with enough age to feel rooted while remaining perfectly comprehensible. Names that sound old suit horticulture better than names that sound new.
The name is available. Enquiries welcome.