Find a self-complementary graph with $v = 8$. Of the $12, 346$ graphs with $v = 8$ only four are self-complementary.

The graph on the left is Fanny. You will find the isomorphisms by matching the vertices of degree 2.

The graph on the right isn't any of the four.

Note that OEIS says there are 10 self-complementary graphs on 8 vertices https://oeis.org/A000171. They are shown in http://mathworld.wolfram.com/Self-ComplementaryGraph.html In fact your graph from the right picture appears there as "8-self-complementary graph 3".

To complement Michal's answer, you can see that your left graph is Fanny Zambuto by keeping the edge relations you have, but by permuting the locations $A \mapsto C \mapsto E \mapsto G \mapsto A$.