Milder versions of oregano are sometimes referred to as ornamental although they also have admirable culinary qualities as well. My personal favorite is Golden Oregano. Golden Oregano has a slightly different flavor than some other varieties, it is pleasant but not as pungent. It works well as a ground cover for landscaping purposes.
Hopflower oregano sometimes called cascading hopflower is primarily used as an ornamental. It produces light green foliage that daintily hang from bowed thin stems. At the end of each stem is minute pink blossom . In the culinary realm it can be used in any dish that calls for oregano, although its flavor is very mild.
Compact Oregano [Origanum vulgaris Compactum] serves as ground cover in many ornamental scenarios. It is a hybrid of marjoram and produces dark green aromatic foliage. It has tubular flowers with conspicuous green bracts from mid summer to early Autumn. Mild flavor.
Mexican Oregano is not as hardy as true oregano and only grows as a perennial in Mexico , the American Southwest and some hot dry southern regions [USDA zones 7b and 11.] it can be grown as an annual anywhere that has reasonably long warm summers. It is suitable for indoor gardens so long as the temperature is kept above 50 F and ample light is provided. It's flavor is similar to common oregano but has a citrus undertone.
Other plants that are also referred to as Mexican oregano include
Lippia graveolens and Plectranthus amboinicus.
Plectranthus amboinicus aka Puerto Rican Oregano, Mexican Oregano, Spanish thyme, Cuban Oregano, Oregano Brujo, and Mexican mint. Zones 9-11. The leaves have a strong oregano like flavor and is commonly used for anything oregano is used for. Also has medicinal qualities and is used in bush medicine in various locales.
Lippia graveolens. Its essential oils contain many of he same compounds found in Oregano giving it a similar flavor. It is related to Mexican Oreagno but not to common oregano.