Hi Mateus,
Let me try to respond as best I can, and comment on what Kokuu added:
1. What is the Mahayana doctrine of the Trikaya? What is the Dharmakaya (is it the same as Emptiness and/or buddha-nature)? What is the Sambhogakaya (is it a transcendental Buddha, like a divine being or something else)? What is the Nirmanakaya (the real, historical Buddha)?
Originally, in the evolution of the concept of "Buddha," there was just Buddha the human being in India, a man, flesh and blood who lived a human life (sometimes noted in English as little "b" buddha). That is Shakyamuni Buddha, also known as Gautama Buddha. A wise and gifted guy (about whom idealized stories began to appear very quickly, likely even during his life), but just "a guy."
Then, the concept developed that
All of Reality, Emptiness, the Wholeness, Boundless which is the
Thusness (which the earthly Buddha realized in Nirvana/Enlightenment) is the real ultimate "Buddha" (with a Big "B") that liberates us. This is the universal or "cosmic" Buddha,
Dharmakaya (the essence body) transcending yet at the heart of all divisions, of which all the separate phenomena of this world ... me and you, this and that, the cat, everything ... are emanations of the Wholeness (including that Buddha guy in India, thus he became the "
Nirmanakaya," which means "emanation body" ... but you, me, the cat, the table, everything are each emanation bodies of the unbroken Dharmakaya Wholeness too). This "Wholeness" is generally also felt to be our (your my and the cat's) ultimate "Buddha Nature" which we had best realize.
Sometime in the development of Buddhism, centuries later than the conception of the above two, very idealized images of "perfect" Buddhas arose ... hyper-human in quality, human in appearance yet beyond all human imperfections, scrubbed clean of all flesh and blood faults, often with super-human powers and abilities ... somehow between the Dharmakaya and Nirmanakaya. The process by which they arose is one example of
hagiography (the process in religion of turning stories/legends of religious heroes gradually into perfect saints). Amida is often considered as one, as is the hyper-idealized "Shakyamuni" (not the historical one) who resided/resides in the fantastic "hyper-India" of the Mahayana Sutras, and countless other such Buddhas. These are the "
Sambhogakaya" (enjoyment body) Buddhas, because they perfectly enjoy their idealized state of realization and perfection. Like the guy in historical India, this is also another facet of the Dharmakaya, which is the "ultimate level." All these Buddhas are other faces of each other ... and you and me too.
Frankly, I have no trouble with the human man in India, and I have no trouble with the "unbroken Reality" that is free of separate self-existence as represented by the "universal" nature Buddha ... but I think that the idealized "enjoyment bodies" are just symbolic, kinda silly, idealized creations of human religious imagination meant to SYMBOLIZE the perfected extremes of what we hope to get out of this practice. They are otherwise malarky and fantasy, extreme romantic creations of the human religious imagination, personifying the idealized qualities of goodness, peace, bliss, wisdom, compassion, power that is the summit of our practice. I am happy to take them as symbols of the Wisdom and Teachings, rather than very literally (but see my comment on Dogen and Keizan, below).
Vairochana is an image of the Dharmakaya "cosmic" Buddha portrayed as a body, sitting cross legged and looking like a human being, which developed because people had trouble with purely abstract notions of a "beyond things and bodies" Dharmakaya. In other words, it is much like that other religion where many folks could not handle some formless notion of an abstract, transcendent "God," so made him a "king with a beard on a throne." Vairochana was needed as an image to give a physical body to a notion beyond physical bodies. Vairochana is just a name and image for what is beyond all name and image. It is kind of silly that they had to give a name and form for this which stands for "no name no form." Even the name and concept "Dharmakaya" is an injustice for what is free of all name and concept. A famous Vairochana is the Giant Buddha in Nara, Japan:
I disagree with Kokuu on the specific use here of Lochana for "Sambhogakaya Lochana." Yes, in the complicated Tibetan/Shingon/Esoteric map of Buddhas, there is a specific female Buddha name Lochana/Locana who is consort to another Buddha, Akṣobhya (or sometimes consort to Vairocana). However, as Okumura Roshi notes in Living by Vow, in Zen, Locana is cherished as the form of Vairocana Buddha who pronounced the Brahma Net Sutra, source of the Bodhisattva Precepts, as the "enjoyment" form of Vairocana. Notice that "Locana" is a short form of "VaiROCANA" without the "Vai." Vairocana means something like "Illuminator" and "Locana" something like "luminating." Tanahashi Sensei, in his "Zen Chants" book, also says that "Locana" is regarded as just another name/form of Vairocana.
Maitreya is the Future Buddha who will come sometime in the future. I believe that Maitreya is regarded as the next earthly Nirmanakaya. I take Maitreya as just a symbol of hope for the future.
If Amida is taken by some school as the "Dharmakaya," then Amida is also the one and the same formless body without body or name ... so "Amida" is also a symbol and convenience to "picture" what cannot be pictured. The name and image of "Amida" is then as silly as the name and statues of "Vairochana."
2. What is the specific Zen and Soto Zen take on the Trikaya? Does Master Dogen or Master Keizan said anything about it?
One might say that it is the main thing that they "riffed" on in their writings (such as Dogen's Shobogenzo), where all this "cast of characters" pops up again and again in their writings. Now, whether they took things "literally" or "figuratively" is not easy to say (likewise when they would riff on the very idealized images of the great Bodhisattvas like Kannon). They just did not think in such terms. So, let me say that (1) the TEACHINGS and WISDOM of Zen and Buddhism are as real as real can be, (2) the idealized Buddhas and Bodhisattvas stand for, embody and symbolize such real-as-real Teachings and Wisdom, thus (3) to that extent, Dogen and Keizan (and me too) believe that these Buddhas and Bodhisattvas are real embodiments of the Teachings and Wisdom. To that extent, all are as real as real can be because the Truths they express are as real as real can be. Amida too, in that sense. Did Dogen and Keizan think that they were more "real entities" than that? Probably, in some sense, I am sure that they did.
Beyond that, Zen Masters leap through ALL words, symbols, concepts of "Buddhas" and "ordinary people" to find the TRUE "Dharmakaya" beyond all that mess of words and ideas, even beyond "Dharmakaya." They leap through the "Trikaya" and the cat and the kitchen sink.
3. What is the relation of the Trikaya with the Dhyana Buddhas of Shingon?
It is not a central concern to most Zen folks. We tend to avoid "how many angels on the head of a pin" questions like that.
4. How can we understand this all in the context of our practice and how does the Verse of Buddha Names should be interpreted as part of our Oryoki practice (or simple daily recitation practice)?
If they are helpful to you to recall these names as an embodiment of the Teachings and Wisdom, do so. In the meal chant, they are just a symbol of our gratitude for the Teachings and Wisdom.
Then, drop their names and all names and sit Zazen!
(sorry to run long)
Gassho, J
stlah