So, I got to thinking about how an enclave of dwarven monks would function. Considering the hierarchy of dwarven loyalty (family-clan-home) I figure that a group of monks would have to mirror that loyalty structure to be effective. I also think it is important to take into account dwarven style (hair, beard, tattoos, scarring/branding, attire, etc.) and dwarven perspective (hatred of orcs, loathing of elves, experience against giants) in how they would describe and develop forms, techniques and styles.
Fundamentally, dwarves should make great monks once you redirect their racially innate commitments to the school/enclave/monastery and style. In human martial arts, most practitioners will switch styles during their training to improve their overall knowledge and understanding, combining aikido with kenpo, judo with nin-jitsu and muay thai, etc. and etc. and etc. But dwarves aren't know for their flexibility and adaptability or acceptance of others. I think using the more traditional separation/competition between martial arts schools when creating the background for a dwarven monk school/enclave/temple/way would be very important. Basically, each school/enclave/"way" is the right path of development and everybody else's "way" is weak and wrong. And, there are always going to be individuals/groups who disagree with one way of thinking and create a new way, thus creating at least 2 competing entities.
Some of the ideas I had for a naming convention for a dwarven monk enclave include:
Way of the Stone Fist (Dimond Axe, Iron Hammer)
Crouching Duergar/Hidden Drow (yes, I totally stole that format)
Order of the Mithril (Golden, Forged, Granite) Heart (Fist, Axe, Hammer)
Path of the Axe and Hammer (Swinging Axe, Crushing Hammer, Blunted Blade, Hammer and Anvil)
Dwarves are not know for their subtly and as such, I would not expect a monkish order to hide who or what they are. Though they may be apt to wear more functional attire when traveling or doing daily activities, robes would probably be standard during organized events. I suspect the leaders of an enclave would adorn their robes with indications of various accomplishments, status symbols and the like - jeweled accents, gold/silver/mithril thread/designs, possibly even jewelry of some sort. I just don't see dwarven monks wearing austere attire.
As for appearance and grooming standards, I can see various teachings being incorporated into different beard/hair designs. One possible option could be using beard length/adornment similar to how human martial arts use a belting system (white-yellow-orange-purple-blue-green-brown-black) to indicate rank/skill. Along those same lines, I can see scarring/branding being used to show commitment to a particular school/way in the same way American football and basketball players get their university or team logo tattooed/branded on themselves.