I got the distribution from the diagram by prolonging the initial $1+$ and $1-$ curves on $Y$, getting the numbers that appeared on the converging points and bolding the prime ones. Then I compared those that appeared on $Y+$ and $Y-$.
I found a similar diagram representing an example of Galois corresponde (Ref. "A Book of Abstract Algebra", Charles C. Pinter):
On the other hand, adding also to $Y+$ and $Y-$ the numbers that converge when prolonging the curves from the point $9$ on $Y$ (I didn't draw thos prolongations on the diagram), the resultant distribution is this another one:
It also can be presented in this way:
I'm almost sure it doesn't have a name(other than what I describe below) since it isn't too interesting.
The curve just places different numbers$\bmod 8$ on $8$ rays from the origin. So, looking at your first distribution, you simply are creating
$$Y^+ = \{n \in \mathbb{N} \mid n \equiv 1,3 \pmod{8} \}$$ $$Y^- = \{n \in \mathbb{N} \mid n \equiv 5,7 \pmod{8} \}$$
It is somewhat interesting that pretty much every prime is on $Y^{+}$ or $Y^{-}$. To be precise, $\mathbb{P} \setminus \{2\} \subset Y^+ \cup Y^-$. But this is obvious when you analyze it, since every prime $p$ except $2$ is odd, so
$$p \not\equiv 0, 2, 4, 6 \pmod{8}$$
And indeed, you forgot to put $2$ in your prime distrubtion.