He is known as all-knowing.
"And what is the miracle of reading minds? There is the case where a monk reads the minds, the mental events, the thoughts, the ponderings of other beings, other individuals, ‘Such is your thinking, here is where your thinking is, thus is your mind.’
"Then someone who has faith and conviction in him sees him reading the minds… of other beings… He reports this to someone who has no faith and no conviction, telling him, ‘Isn’t it awesome. Isn’t it astounding, how great the power, how great the prowess of this contemplative. Just now I saw him reading the minds… of other beings…’ SuttaCentral
This was said by the Blessed One, said by the Arahant, so I have heard: "The world has been fully awakened to by the Tathagata. From the world, the Tathagata is disjoined. The origination of the world has been fully awakened to by the Tathagata. The origination of the world has, by the Tathagata, been abandoned. The cessation of the world has been fully awakened to by the Tathagata. The cessation of the world has, by the Tathagata, been realized. The path leading to the cessation of the world has been fully awakened to by the Tathagata. The path leading to the cessation of the world has, by the Tathagata, been developed.
"Whatever in this world — with its devas, Maras, & Brahmas, its generations complete with contemplatives & brahmans, princes & men — is seen, heard, sensed, cognized, attained, sought after, pondered by the intellect, that has been fully awakened to by the Tathagata. Thus he is called the Tathagata.
"From the night the Tathagata fully awakens to the unsurpassed Right Self-awakening to the night he is totally unbound in the Unbinding property with no fuel remaining, whatever the Tathagata has said, spoken, explained is just so (tatha) and not otherwise. Thus he is called the Tathagata.
"The Tathagata is one who does in line with (tatha) what he teaches, one who teaches in line with what he does. Thus he is called the Tathagata.
“In this world with its devas, Maras, & Brahmas, its generations complete with contemplatives & brahmans, princes & men, the Tathagata is the unconquered conqueror, all-seeing, the wielder of power.[2] Thus he is called the Tathagata.” This is the meaning of what the Blessed One said. So with regard to this it was said:
Directly knowing all the world,
all the world as is really is,
from all the world disjoined,
in all the world unmatched:
Conquering all
in all ways,
enlightened,
released from all bonds,
he touches the foremost peace —
Unbinding, free
from fear.
He is free of fermentation,
of trouble,
awakened,
his doubts cut through;
has attained the ending of action,
is released in the destruction of acquisitions.
He is blessed, awakened,
a lion, unsurpassed.
In the world with its devas
he set the Brahma-wheel going.
Thus divine & human beings
who have gone to the Buddha for refuge,
gathering, pay homage
to the great one, thoroughly mature:
‘Tamed, he’s the best
of those who can be tamed;
calm, the seer
of those who can be calmed;
released, supreme
among those who can be released;
crossed, the foremost
of those who can cross.’
Thus they pay homage
to the great one, thoroughly mature:
'In this world with its devas,
there’s no one
to compare SuttaCentral