How to name this quintuply-bonded chromium dimer?
It was a great effort. However, in the proposed name


  bis[(μ-2,6-{[2,6-di(1-methylethyl)]diphenyl}phenyl-1κC1,2κC7)chromium](5&nbsp;Cr—Cr)


I can see several issues:


In you point 12: Forcing the metal-metal bond multiplicty in the name is interesting, however I wouldn't go against the rules. See the example with the multiple (triple) Cr-Cr bond, in the rules:


  IR-10.2.5.1 The eta (η) convention
  (…)
  Example 26.
  
  
  (μ-2η4-buta-1,3-diene-1,4-diyl-1κ2C1,C4)carbonyl-1κC-bis[(η5-cyclopentadienyl)chromium](Cr—Cr)


not "…(3&nbsp;Cr—Cr)".

The purpose of the rule seems to be to just specify (only) the connectivity, i.e. the count of such and such metal-metal connections.


  IR-9.2.5.6 Trinuclear and larger structures
  (…)
   Example 6.
  
  octacarbonyl-1κ4C,24κC-bis(triphenylphosphane-3κP)-triangulo-diironplatinum(Fe—Fe)(2&nbsp;Fe—Pt)


One could speculate that they, to denote the bond order as well, intend to use a multiplied Em dash character variants, which are non-existent presently.

Another motivation might have been that the bond nature / bond-order is often disputed in organometallics.
Your name can denote a different isomer (though maybe impossible), with the two ligands oriented the same way, not say antiparallel, or head-tail, but head-head. I.e. one of the ligand flipped, and connected to chromiums the other way.

From the rules:


  IR-10.2.5.1 The eta (η) convention
  (…)
  Example 24.
  
  
  (μ-1η5-cyclopenta-2,4-diene-1,1-diyl-2κC)(μ-2η5-cyclopenta-2,4-diene-1,1-diyl-1κC)bis[(η5-cyclopentadienyl)hydridotungsten]


not bis(μ-1η5-cyclopenta-2,4-diene-1,1-diyl-2κC)bis[(η5-cyclopentadienyl)hydridotungsten].

I.e. repeating the ligands name, with the 1/2 metal locants swapped. Which, however, is obviously inconvenient, maybe the rules will be improved in the future to somehow support relative locants, or so.
2,6-{[2,6-di(1-methylethyl)]diphenyl}phenyl part (you construction in points 3, 4) is weird.

The standalone ligand residue would be named according to the organic chemistry nomenclature:


2,6-bis[2,6-di(1-methylethyl)phenyl]phenyl, more correctly
2,6-bis[2,6-di(propan-2-yl)phenyl]phenyl

Inorganic nomenclature does not have so strict "preferred name" concept. Table IR-10.1 lists isopropyl as an acceptable alternative name for the propan-2-yl. So I would go with 2,6-diisopropylphenyl instead of 2,6-di(1-methylethyl)phenyl or , to not complicate the name further.
Problematic locant for the kappa notation in the ligand 2,6-{[2,6-di(1-methylethyl)]diphenyl}phenyl-1κC1,2κC7. Maybe a prime symbol / apostrophe could be used like in biphenyls, terphenyls..

I think it should be rewritten to more verbose, but unambiguous 2-(2,6-diisopropylphenyl-1κC1)-6-(2,6-diisopropylphenyl)phenyl-2κC1 (both locant superscripts after κC's are now 1, but its not a problem).


And one note:


Even though the rules state


  IR-9.2.4.3 Comparison of the eta and kappa conventions
  
  The eta convention (Section IR-10.2.5.1) is applied in cases where contiguous donor atoms
  within a given ligand are involved in bonding to a central atom. Thus, it is used only when
  there is more than one ligating atom, and the term η1 is not used.


in the literature(web) for the structure with a more complicated ligand


  


featuring the similar 2,6-di(iPr)Ph···Cr bond, the following shortcut is used


  Ar′Cr(μ2:η1,η3-N3(1-Ad))CrAr′


which contains the η1 (and, it interestingly relates to the NNN part of the ligand on the right, not to the phenyl). But I'm not gonna use it in the proposed name.


So my candidate name is
[μ-2-(2,6-diisopropylphenyl-1κC1)-6-(2,6-diisopropylphenyl)phenyl-2κC1][μ-2-(2,6-diisopropylphenyl-2κC1)-6-(2,6-diisopropylphenyl)phenyl-1κC1]dichromium(Cr—Cr)

Finally, lets mention the paper in which this interesting compound was described: Nguyen, T.; Sutton, A. D., Brynda, M.; Fettinger, J. C.; Long, G. J.; Power, P. P. Synthesis of a Stable Compound with Fivefold Bonding Between Two Chromium(I) Centers. Science 2005, 310 (5749), 844–847.