As the sister-city of Gabil-gathol in the Blue Mountains, Tumunzahar was south of Mount Dolmed.  The Elves called it Nogrod, and it is translated into English as "Hollowbold".  I've seen it typically analyzed as tumun "hollow" and zahar "bold", following the same word order as "Hollowbold".  However, once you really look at the word forms and understand Tolkien's interest in etymology, the reverse makes far more sense.

To understand how and why tumun is "bold", we have to know just what "bold" is! Bold is an Old English word roughly meaning "house". I've seen it explained as being a "building" or "dwelling", and especially of the large, prominent sort. It's associated with another Old English word, byldan, which was a verb "to build".  In the word Khazad-dûm, we have dûm which is "excavations, halls, mansions", and Tolkien also used "delvings".  A mansion is a "large,
impressive, or stately residence" or a "large building with many apartments".  In archaic usage, it was simply "an abode or dwelling place." (Reference quotes from The Random House Dictionary)  From that standpoint, it's fairly easy to see that a "mansion" is comparable with a "bold".  Additionally, the idea of excavation and delving underground being a part of the definition of dûm is very similar to how byldan "to build" is related to bold.  In these words, we have the whole notion of Dwarves delving underground to construct dwellings running in perfect parallel with human notions of building.  To me, this is Tolkien's linguistic genius at its finest.

The next step is to see how we arrive at the given word forms.  Tumun and dûm start with different sounds, <t> and <d>.  As shown in the discussion on Khazad-dûm, Felak-gundu is sometimes written as Felag-gundu, showing voicing assimilation, so we know that Khuzdul does this in at least some circumstances.  Arabic has
-dt- -dd-.  If this is also the case in Khuzdul, then dûm would actually be tûm, with the <t> assimilated in voicing to become <d>.

Tolkien wrote that dûm (tûm) is
"either a true plural or a collective".  The form can be seen as following the same template as Khuzd, Khazâd.  In Arabic, "geminate" or "doubled" roots, where the 2nd & 3rd radicals are the same, such as T-M-M, this form is a possible result.  The root T-M-M would take the template CuCC, giving tumm.   In those situations, Arabic contracts the form to CûC, or tûm in this case.  From this, we can view tûm as singular in form, so describing it as a collective makes sense.

Arabic makes use of collectives a fair amount.  For those nouns that are collective (that is, they are singular in form and plural in meaning), Arabic adds a suffix to the word to indicate a single item of that type.  A couple examples are baqar "cattle", baqarah "a cow" and jund "army", jundi "a soldier".  The words that indicate the single item are known in Arabic as "nouns of unity", and in grammar is called a "singulative number".  Looking at tumun, we still have to figure out where the final -un comes from, and the suffixes of Nargûn and Tharkûn are immediately comparable.  In those cases, -ûn seems to indicate a specific entity characterized by the root meaning.  A singulative suffix marks a single item, so the two seem very comparable.  Looking closer at this, we can see that tûm would have a likely composition form tum.  Add the suffix and we get tumûn.  Finally, put tumûn into the composition form, probably tumun, to combine it with zahar to form a compound word.  Voila!

From all this, we have tumun as "
excavation, hall, mansion" and singulative, nominative, composition.

On a side note, the concept of the root G-N-D (from gund) also seems to be somewhat similar to the concepts found in Khazad-dûm and Tumunzahar, which is of delving, excavating, and building.  G-N-D denotes concepts of the process of delving/excavation/tunneling, as seen by the verb gunud.  The result, a single underground hall, would be gund It could be seen as similar to how we think of one room in a house.  One or more ganâd (using the Khuzd, Khazâd template) that are designed for a single purpose and are considered part of a unified whole would be a tumûn "a bold, a mansion, a delving or excavation".  Tumûn would refer to the more general stucture, or the "house" to extend the "room vs. house" analogy.  Again, this fits in very well with the notion of a "mansion", and we can see exactly why Tolkien chose this term.  A whole series of these would be the collective tûm "mansions, delvings, excavations", and would be an entire underground town, city, or other settlement constructed by the Dwarves.

Zahar is then "hollow", following the adjective patterns of other words, although it could also have a verbal root (a "state" verb).  Zahar should be singular, nominative, indefinite.

Tumunzahar then is "a mansion, delving, or excavation of hollowness", or "Hollowbold", and is a construct compound word of noun-adjective word order.

The Silmarillion, ch 10, pg 91
The War of the Jewels, pg 209, 389