Baring some great philosophers of language, like Wittgenstein, Derrida, and say Walter Benjamin, Buber, etc., most modern folk don't appreciate the relationship between the spirit and the word. A word is always a name, a naming, whereby, as Wittgenstein implies, the spirit of a thing is baptized into the name (or the name baptized into the spirit) thereafter creating a union that incarnates the invisible spirit of the thing with the visible name that reference the invisible spirit. The writers of the midrash in question are precursors of men like Wittgenstein and Benjamin, such that they realize something of the spirit of a thing is always hiding beneath the name of a thing.
When Adam names himself before God and the angels he's providing a link to the spirit of man. When Adam names god before God and the angels, he's revealing a link to the spirit of God.
So what does Adam name himself? He names himself alef-dalet-mem א–דם. . . Why separate the alef from the dalet-mem? The alef is the first letter, and as the first letter it represents the first creation of God, that thing, even letter, closest to God. Adam (אדם) is firstly related to the alef, God, such that the first letter in his name is the alef. ----- So what of the dalet-mem? ------ It spells blood דם (dam). Adam is God's blood? Yes. According to midrashim he is:
8. OF THE GROUND (ADAMAH), R. Berekiah and R. Belbo in the name of Samuel the Elder said: He was created from the place of his atonement, as you read, An altar of earth (adamah) thou shalt make unto me (Ex. xx,21). The Holy One, blessed be He, said: `Behold I will create him from the place of his atonement, and may he endure!"
Midrash Rabbah, Bere****h XIV.8.
God creates an altar of earth, and spills (breathes, metzitzah) his blood into and onto the altar of earth (adamah). Adam's name is related to "earth" (adamah), and the color "red" (adam) since, according to midrashim, Adam is created as an altar of earth infused with the breath of life. . . But what does the breath of life have to do with blood? . . . Immediately after suggesting that Adam is created as an earthen altar, a place of atonement (so that he might endure when the need for atonement comes, since it's produced in his very creation) the midrash speaks of the fact that the breath of life (mixed with the earthen altar) has five names:
THE BREATH OF (NISHMATH) LIFE. It has five names: nefesh, neshamah, hayyah, ruah, yehidah. Nefesh is the blood: For the blood is the nefesh --- E.V. "life" (Deut. xii, 23). Ruah: this is so called because it ascends and descends: thus it is written, Who knoweth the ruah (E.V. "spirit") of man whether it goeth upward and the ruah, of the beast whether it goeth downward to the earth (Eccl. iii, 21)? Neshamah is the breath; as people say, His breathing is good. Hayyah (lit. "living"): because all the limbs are mortal, whereas this is immortal in the body. Yehidah (unique) : because all the limbs are duplicated, whereas this is unique in the body.
Ibid. XIV.9.
Rabbi Hirsch clarifies this:
. . . the primary meaning of דם [blood] is image, symbol, representative . . . The animal soul--- together with the body--- is formed from the earth. By contrast, the source of man's soul is not the source of his earthly frame; rather, God, as it were, breathed into man a spark of His Own essence. . . your blood, which belongs to your souls, is Mine, not yours. I will demand it, because it belongs to Me and is at My disposal, and I require a reckoning for every drop of your blood. . .When God says אדרש [I require] regarding the blood consigned to the human soul, He declares that our blood belongs to Him.
Hirsch Chumash, Bereshis 9:5.
The animal body, which Rabbi Hirsch associates with our natural conception, at night, through Gen(i)tile sex, is from the earth, represents the earth, is earthen: in the case of the Jew its literally an altar prepared for sacrifice. On the other hand, the blood of the Jew, is not associated with the earth, i.e., Gen(i)tile sex. It's from God--- such that the earthen altar is prepared from the earth, as animal flesh (the Gentile), so that on the eighth day, a sacrifice takes place such that the very organ the ancients associated with god, the god of the phallic-cults, is sacrificed, and its blood spilled on the earth altar in order to form a Jew from the sacrifice of the pagan god, its blood, and it's mixture with the earthen altar. The blood of the pagan god, the phallus, the serpent, is spilled on the altar of earth, earth conceived by the serpent, such that the mixture of this blood and this earth, creates the Jew, who is born-again on the eighth day, of a process that atones for the very nature of his first birth, through the serpent, in that the "blood" (death) of this pagan god (the serpent), when mixed with the earth, creates the essence of the Jew.
These things are all implicit in the midrash in question. When Adam names himself "blood of god" alef---dalet-mem א––דם, he is setting the stage for the second revelation (the name of God) that retroactively feeds back into his own name, thereby completely justifying all the foregoing, if you will, but naturally you won't.
John