Here is a further exposition of the meaning of the Tathagatha from the Aganna sutta, DN:
Yassa kho panassa, vāseṭṭha, tathāgate saddhā niviṭṭhā mūlajātā patiṭṭhitā daḷhā asaṃhāriyā samaṇena vā brāhmaṇena vā devena vā mārena vā brahmunā vā kenaci vā lokasmiṃ, tassetaṃ kallaṃ vacanāya – ‘bhagavatomhi putto oraso mukhato jāto dhammajo dhammanimmito dhammadāyādo’ti. Taṃ kissa hetu? Tathāgatassa hetaṃ, vāseṭṭha, adhivacanaṃ ‘dhammakāyo’ itipi, ‘brahmakāyo’ itipi, ‘dhammabhūto’ itipi, ‘brahmabhūto’ itipi.
2] He whose faith in the
Tathágata is settled, rooted, established, solid, unshakable by any ascetic or Brahmin, any
deva or mara or Brahma or anyone in the world, can truly say: "I am a true son of the
Blessed Lord, born of his mouth, born of Dhamma, created by Dhamma, an heir of
Dhamma." Why is that? Because, Vasettha, this designates the Tathágata: "The Body of Dhamma," that is "The Body of Brahma,"  or "Become Dhamma," that is "Become
I just have one problem with the translation, what is "bhuto" in Buddhism? Does it mean to become?