In China, regarding the identity of the Zen or Ch’an school, it is distinguished only by the Zen transmission lineage. This is because in China there is no special ordination for Zennists. One is simply ordained a Buddhist monk or nun of no particular sect (this is different in Japan). (In the U.S. some who claim they’re following a Zen tradition because they’ve received the typical Chinese monastic ordination, don’t seem to understand how Chinese Buddhism works.)
As Buddhist scholars point out, going back to the Sung Dynasty and even today, the huge majority of monks and nuns in China were not affiliated with any particular Buddhist school. Still a tradition in China, the key to becoming a member of the Zen lineage, eventually receiving the seal of transmission from a Zen master, is first to become his personal disciple. It is not in error to say that this is not an easy task as compared with becoming a monk or a nun.
As for the importance of the Zen transmission, in order to become the abbot of a designated Zen monastery, one had to be first transmitted. In other words, the special importance of the Zen transmission is only meaningful and advantageous for someone wanting to become the abbot of a large public Ch’an monastery. Also, it is important to understand that “Ch’an monastery” did not mean the huge majority of monks and nuns, including lay people, who practiced at this monastery received Zen transmission. Far from it.
Zen in North America and Europe is not like Chinese Ch’an/Zen. One is first ordained a Zennist who then follows a Zen regimen of meditation (zazen) and koans. Basically, to be blunt, this is a pile of bovine manure. Minus the Zen transmission, which begins with Mahakasyapa who, according to the Avatamsaka Sutra, is not capable of perpetuating the lineage of Buddhas, there is nothing special about Zen institutions.
The only authentic transmission is Mind to Mind, not teacher to student. If certification is further required then, as I used to say years ago, find a leaf with a bird shit seal on it. Of course you might do what Dogen did, forge your own certificate.