Naming of asymmetric organic molecules with two nitroxides
The structure can be redrawn somewhat more clearly:


  


Let's call the basic structure, where R1 = R2 = H, ‘the skeleton’.

If your name was, after fixing some enclosing parentheses to square or curly brackets, even the ‘preferred IUPAC name’, it's not a nice one, because it does not reflect the symmetry of the skeleton, and repeats the TEMPO and adamantane building block names.

(From now on, I'm gonna use the blockquote for IUPAC organic nomenclature rules 2013 generated names, or the book citations, if section name included.)

"Almost preferred" IUPAC name, substituted carbamoyl biphenyl dicarboxamide

The skeleton is named


  
  N4,N4′-dicarbamoyl[1,1′-biphenyl]-4,4′-dicarboxamide.


This preferred name is obviously based on the biphenyl dicarboxylic acid diamide


  
  [1,1′-biphenyl]-4,4′-dicarboxamide


substituted with carbamoyl ($\ce{NH2-CO\bond{-}}$) groups at each nitrogen.

Simple monosubstituted derivatives of the skeleton (there are only two kinds of them initially) are named


  
  N4,N4′-dicarbamoyl-N4-methyl[1,1′-biphenyl]-4,4′-dicarboxamide


and


  
  N4-carbamoyl-N4′-(methylcarbamoyl)[1,1′-biphenyl]-4,4′-dicarboxamide.


R2 (“TEMPO-4-yl”) can be named,


  
  2,2,6,6-tetramethyl-1-oxylpiperidine-4-yl (group)


according to the rules of making the radical to be prefix (e.g. when there is yet more prioritized radical):


  P-71.5 Prefixes denoting radicals
  
  (…)
  
  Examples:
  
  (…)
  
  $\ce{-O^.}$
  
  oxyl (preselected prefix)
  ylooxidanyl
  &nbsp;&nbsp;(not ylohydroxy)
  
  (…)
  
  P-71.7.d.1 (…) 
  
  
  
  (3-oxylbenzoyl)oxyl (PIN)
  [3-(ylooxidanyl)benzoyl]oxidanyl


however the rules do not make a good distinction between residues (prefixes) and radicals.

So the resulting name would be
N4-(adamantan-1-yl)-N4′-[(adamantan-1-yl)carbamoyl]-N4′-(2,2,6,6-tetramethyl-1-oxylpiperidine-4-yl)-N4-[(2,2,6,6-tetramethyl-1-oxylpiperidine-4-yl)carbamoyl][1,1′-biphenyl]-4,4′-dicarboxamide. But it still redundantly repeats some building block names.

Unfinished IUPAC name based on substituted "diallophanylated biphenyl"


  P-66.1.6.1.1.4 Carboxylic acid derivatives of urea
  
  Two carboxylic acids are related to urea; have been known as ‘allophanic acid’ for $\ce{H2N-CO—NH-COOH}$ and ‘hydantoic acid’ for $\ce{H2N-CO-NH-CH2-COOH}$. These names are no longer recommended. Preferred IUPAC names for these two acids and their derivatives are formed systematically.
  
  Examples:
  
  $\ce{H2N-CO—NH-COOH}$
  carbamoylcarbamic acid (PIN)
  (aminocarbonyl)carbamic acid
  
  $\ce{H2N-CO—NH-CO\bond{-}}$
  carbamoylcarbamoyl (preferred prefix)
  [(aminocarbonyl)amino]carbonyl


The allophanoyl- prefix can be found in the older IUPAC 1979 nomenclature, rule C-971.

The skeleton could be named


4,4′-diallophanoyl[1,1′-biphenyl], or
4,4′-bis(carbamoylcarbamoyl)[1,1′-biphenyl],


if you want.

But now we would have to repeat the two differently substituted allophanoyls in the name. Or derive a name from the symmetrical one, but how to number it?

Urea based IUPAC name

Closer look at your structure reveals that it in fact is two N,N′ asymmetrically substituted urea


  P-66.1.6.1.1 Urea and its substitutive derivatives
  
  P-66.1.6.1.1.1 The compound $\ce{H2N-CO-NH2}$ has the retained named ‘urea’, Which is the preferred IUPAC name, With locants N and N′, as shown above the structure below. The systematic name is ‘carbonic diamide’. The locants 1, 2, and 3 have been used in the past and may be used in general nomenclature.
  
  $$\begin{array}{ccc}
\ce{H2\overset{$N$}{\underset{1}{N}}-\underset{2}{C}O-\overset{$N'$}{\underset{3}{N}}H2} &amp; \hskip{3em} &amp;
\ce{H2\overset{$N$}{N}-CO-\overset{$N'$}{N}H2} \\
\text{urea (PIN)} &amp; &amp;
\text{carbonic diamide}
\end{array}
$$
  
  $$\bbox[0.5em,border:1px solid black]{\text{Numerical locants for urea are no longer used in the IUPAC preferred names.}}$$


molecules, N,the-other-one's-N′-interconnected with


  
  [1,1′-biphenyl]-4,4′-diyldicarbonyl (group).


And that's a correct name, used e.g. in


  
  2,2′-([1,1′-biphenyl]-4,4′-diyldicarbonyl)dipropanoic acid.


(If these propanoic acids were interconnected by different carbons, 2,3′ (there's no other option), such multiplicative name would be no longer a preferred one; see e.g. P-15.3.2.1.1. But never mind, we're making a nice one.)

The skeleton now can be named ([1,1′-biphenyl]-4,4′-diyldicarbonyl)diurea. (More precisely N,N′-([1,1′-biphenyl]-4,4′-diyldicarbonyl)diurea. Or N,N′′-…? And what about such multiplicative names of asymmetrical derivatives? There's no definitive answer, but this would be for another question.)

So we'll use the other urea numbering, the numerical, non-preferred one.

Now we get a nice name:
1,3′-([1,1′-biphenyl]-4,4′-diyldicarbonyl)bis[1-(adamantan-1-yl)-3-(2,2,6,6-tetramethyl-1-oxylpiperidine-4-yl)urea]

(But I would like similarly short and non-redundant name that would end like “…bis[(2,2,6,6-tetramethylpiperidin-1-yl)oxidanyl]” yet more.)