Yes, both Human and Liv (to use translations instead of transliterations) show us who we are. My one quibble with your earlier expression of this would be calling adam “man.” If it were ha’ish (?) and ha’ishah that would be justified, but ha’adam isn’t a sexed term like those. It marks species or kind, not gender or sex.
The Eden story refers to the human and later the help or ally for the human, both times using masculine terms. That doesn’t mean the human and the future helper are both male. Hebrew requires grammatical gender. Since there’s no neuter, the masculine typically gets used when gender is irrelevant or mixed or unknown. We don’t get gender reveals until the poem later on. “She will be called woman, for she was taken from man” uses the standard words ish and ishah for man and woman. Only here do we see that the remaining side of the human is a man while the helper built from the side that was taken is a woman.
A good analogy for this assymetry between Human and Liv is the difference between Israel and Judah. As names of nations, Israel and Judah are a lopsided pair. It’s obvious what nation “Judah” refers to. When both names appear together, they clearly identify the southern and northern kingdoms. But “Israel” on its own may refer to the early undivided nation, the northern kingdom, both separated nations, or even to Judah on its own.
Just as some of Israel split off to become the nation of Judah, God split off a side of Human to form Liv. These special parts, Judah and Liv, are not less than their counterparts who continue to be known by more common names. “Liv” refers to the woman we meet in Eden. “Human and Liv” are the first man and woman. But “Human” without Liv is just as plastic as “Israel” without Judah. It may reference the man, the first couple, the undivided first human or humans generally. Even as Genesis blends these dimensions into one character, Human remains a more blurry figure than Liv.
But, you can see why I prefer to call them Human and Liv rather than Adam and Eve, since “Adam” in our culture has become a standard name for a man. That’s a significant way Adam in English differs from the blandly generic adam in Hebrew.