What are the Lewis structures for hydrogen cyanide and cyanogen??

I think it's

H:C:::N

:N:::C:C:::N:

with the inner upper electrons being shared.

For the elements in these compounds, which is the noble gas whose electron configuration is attained in the Lewis structures?

(CN)2 is ok.
You have omitted two electrons on HCN.
Count it this way.
H has 1 electron in its outer shell.
C has 4 electrons in its outer shell.
N has 5 electrons in its outer shell.
Total 1 + 4 + 5 = 10 electrons.
You have accounted only for 8.
H:C:::N:

Now look at the periodic table and identify the NEXT higher noble gas for H, C and N.

Is it Ne, Neon?

It is for C and N. Not for H.

For H, will it be He?

yes.

Thank you