Christphany is from the Greek noun Christos- "Christ, Anointed", and the Greek ending "phany" from the verb phaneroō, to be revealed or to manifest. So, it is Christ made known and clear to the eye. So, one was Christophany.
Just to confirm that the other two were angels and the third was the LORD (YHWH)
We put Chapters 18 and 19 of Genesis together.
First let's start with Genesis 18 vs 2
vs 2 "When he lifted up his eyes and looked, behold, three men were standing opposite him..."
The word "men" is the Hebrew word "ish" which actually is not merely used for people but for animals and angels it is a way of saying male (masculine features). Thus this tells us that they were not "adam" or from the soil.
Secondly we set our attention to the following verses of Genesis 18 vs 9-10 & vs 22
vs 9 Then they said to him, “Where is Sarah your wife?” And he said, “There, in the tent.” vs 10 He said, “I will surely return to you at this time next year; and behold, Sarah your wife will have a son.”
vs 22 "Then the men turned away from there and went toward Sodom, while Abraham was still standing before the Lord."
I want to point out two things:
1) that one of the men says that he will return and Sarah will have a son.
2) The men have departed to Sodom and the LORD (YHVH) has stayed behind and is still talking to Abraham.
First point: the "man" that says he will return to Sarah we see is the LORD himself as we find in Genesis 21 vs 1
vs 1 "And the LORD visited Sarah as he had said, and the LORD did unto Sarah as he had spoken."
Now Second point: Genesis 19 vs 1
vs 1 "Now the two angels came to Sodom in the evening as Lot was sitting in the gate of Sodom. When Lot saw them, he rose to meet them and bowed down with his face to the ground."
We can make the math two angels are in Sodom (we will see that they are called men or "ish") these angels that are in Sodom are the "men" that left for Sodom in Genesis 18:16 (quoted above) but we only see 2 of the three meaning the third had to be the LORD (YHWH)
Now to confirm that the angels are called men it is confirmed by Genesis 19 vs 12 "Then the two men said to Lot, “Whom else have you here?" We see that same word "ish" not "adam", in Hebrew, is used thus we can conclude two of the three "ish" left to Sodom two being angels and the third "ish" being YHWH himself!