Nomenclature in case when same fucnctional group is present more than once
The IUPAC rules do not seem to have an explicit rule for general cases when more than two cyano groups are attached to the (linear) alkane chain, like it does for aldehydes (see Is propane-1,2,3-tricarbaldehyde the correct IUPAC name of CHO-CH2-CH(CHO)-CH2-CHO?), but do have a related one:


  P-66.5.1.1.2 If an unbranched alkane is linked to more than two terminal cyano groups, all cyano groups are named from the parent hydride by the substitutive suffix ‘carbonitrile’, preceded by appropriate multiplying prefix and locants.
  Example:
  
  $\ce{\overset{4}{C}H3-[CH2]2-\overset{1}{C}(CN)3}$
  butane-1,1,1-tricarbonitrile (PIN)


I think that similar usage in general is implicitly allowed in the rule


  P-66.5.1.1.4 When a group is present that has priority for citation as the principal characteristic group or When all $\ce{-CN}$ groups cannot be expressed as the principal characteristic group, the $\ce{-CN}$ group is designated by the preferred prefix ‘cyano’.
  
  (…)


(Three examples follow, two of them have another higher-priority group $\ce{-COOH}$; the other one has three cyano groups, not on linear chain but one of them is attached via a chain branch, $\ce{NC[CH2]2CH(CH2CN)[CH2]2CN}$, 4-cyanomethyl(heptanedinitrile).)

I our case, we can express all the groups as principal characteristic group, so the correct name should be propane-1,2,3-tricarbonitrile.