Azaghâl was the Lord of Gabil-gathol (Belegost) in the First Age. He led the dwarves into the Battle of Unnumbered Tears, where he was slain by the dragon Glaurung. However, he managed to wound Glaurung to such a degree that the beast had to retreat from the battle field. Azaghâl's dwarven subjects then carried his body away while singing a dirge, and no one dared to stop them.
Glaurung first emerged in the year First Age 260, during the Siege of Angband, and he was driven back by Fingon because he was not yet fully mature. Sometime soon after this, the dwarf smith Telchar created what became known as the Dragon-helm of Dor-lómin. The crest was shaped like the head of Glaurung. The helm was wrought for Azaghâl, and he wore it until he gave it to Maedhros as a reward for having saved Azaghâl's life. It was because of that that Azaghâl did not have the Dragon-helm when he finally faced Glaurung in the Battle of Unnumbered Tears, and it is perhaps because of this that Azaghâl was slain.
Nowhere are we told what the name Azaghâl means. Because Azaghâl was a dwarf and the letters in it are found elsewhere in Khuzdul, it is generally assumed to be Khuzdul in origin. However, the Dwarves had secret, "inner" names that they didn't reveal to anyone. "Not even on their tombs did they inscribe them." Why then does a Khuzdul name appear for Azaghâl?
If we look at Arabic names as an example, one part of the name is called the laqab, which is a descriptor of the person. For example, as part of their full name a person might be called al-Râshid, which is "the Righteous". Not everyone will necessarily have a laqab as part of their name. We actually see this exact sort of naming convention with the Dwarves, as with Thorin Oakenshield and Dain Ironfoot. The comparison to Arabic continues with the use of patronymics, where Dwarves often introduce themselves in the manner of "Gimli son of Gloin", or as seen on Balin's tomb inscription: Balin Fundinul. Sometimes Arabs will use multiple patronymics in their name, as does "Thorin son of Thrain son of Thror". The secret, "inner" names used by the Dwarves are what Arabic would consider to be the ism portion of a name: the "personal" name, as we would call it in English. The use of a descriptive title or name (a laqab) may have grown out of the Dwarves' very secrecy about using their personal names (ism) with those of other races. My guess then is that the names we see of the First Age Dwarves of the Ered Luin, Azaghâl, Telchar, and Gamil Zirak, are each a descriptor, or "laqab". The Dwarves of Khazad-dûm eventually developed the custom of taking an outer personal name from the surrounding Mannish cultures as well as using a descriptive name. This additional practice would explain why we see only Khuzdul names from the Dwarves of Gabil-gathol and Tumunzahar, while all of the names of Durin's Folk were represented by names from Scandinavian myth.
A common assumption has been that Azaghâl is perhaps - or probably - related to the Adunaic word azgarâ "to wage war". This is based on the observation that both have a <z> and <g>, and also start with an <a> (or starts with the glottal stop <'> if you prefer). Following this idea, it is suggested that -âl may be an agentive suffix, such that azagh- might mean "to war" and Azaghâl would be "warrior". There is an apparently related Adunaic word, zagar, which could mean either "warrior" or "sword". It is found in the name of the Numenorean king Ar-Belzagar. His name in Quenya is Tar-Calmacil, which means "King Light-sword". Because the names of the Numenorean kings were usually a direct translation between Quenya and Adunaic, it's very possible that zagar is then "sword". The verb azgarâ would perhaps mean "to raise or use swords against", and thus lead to the translation "to wage war". It is possible that zagar is simply "warrior", though, given the probable relation to azgarâ.
Either way, I think it's improbable that Azaghâl shares a similar meaning. If -âl is a suffix, then the root is '-Z-Gh, which differs from the Adunaic root Z-G-R to a fair degree. I am also not aware of suffixes in Semitic languages that tend to be used as agentive or professional markers. In Arabic, for example, an active participle will generally take on an agentive meaning, and I've seen a t- prefix used to derive words that have a social or professional meaning.
Another issue is whether <gh> is a phoneme in Khuzdul at all. As I explain in the phonology section, there are most certainly not "voiced aspirates" in Khuzdul. Biblical Hebrew, Arabic, and Adunaic all have the voiced velar fricative /ɣ/, which Tolkien generally writes as <gh>. However, Modern Hebrew and Yiddish do not have it. Both of those languages have an unvoiced fricative, the velar /x/ for Modern Hebrew and uvular /χ/ for Yiddish. Both also have a rhotic /r/ which can be realized as a uvular trill /ʀ/. This is also true for Khuzdul, which can have the uvular trill and has an unvoiced palatal fricative /ç/, which is written <hy>, instead of the velar or uvular fricative. In The Lord of the Rings Appendix E, Tolkien writes that <gh> is a voiced fricative in Black Speech and Orcish, but no mention is made of Khuzdul. The name Azaghâl is the only example we have were <gh> shows up in Khuzdul. Since the -âl doesn't recall any Semitic agentive suffixes, and there is no vocalization pattern in Arabic similar to aCaCâC that we see in Azaghâl, it seems less likely that <gh> is indeed a phoneme in Khuzdul. If Khuzdul also lacks the voiced velar fricative <gh>, it would make the language quite similar to Modern Hebrew and Yiddish, at least in this range of consonants. In my view, it seems very likely that Tolkien would have been familiar with the Ashkenazi Jews of Germany, heard their language, and wanted Khuzdul to mimic that to some extent.
All of this points to the possibility that Azaghâl could be split into two elements: azag and hâl. This immediately looks more like other example Khuzdul words and also mimics Arabic morphology more closely. The question then is, what would these two words mean?
Going back to the idea of the Arabic laqab and what we know about Azaghâl, the best I can propose is that azag is "dragon" and hâl is "helm". It seems that the Dragon-helm of Dor-lómin may have been something of a status symbol for Azaghâl, given that Telchar wrought it, "on it were graven runes of victory", and it had a power "that guarded any who wore it from wound or death". It was thus worthy as a payment to Maedhros for saving his life. With the image of Glaurung on the helm's crest, it would be quite recognizable, and so Azaghâl could quite easily have come to be closely associated with the helm, and it with him. For those reasons, it seems fitting that Azaghâl would have come to be known as "Dragon-helm", similar to how Thorin was "Oakenshield".
Because the helm "struck fear into the hearts of all beholders", I strongly considered the possibility that Azaghâl might mean "Dread-helm". However, Turin was eventually known by that name when he came to wear the helm, and it seems more likely that Azaghâl's name would mean something different. "Dragon-helm" also seems, to me, to be a more "glorious" name, more fitting for a dwarf-lord. Azaghâl could quite easily have any number of meanings other than "Dragon-helm". However, it is at least logical and fits what little circumstantial evidence there is. In lieu of any further information, it's my best guess.
Azag is then "dragon" and is singular, nominative, composition.
Hâl is "helm" and is singular, nominative, indefinite.
The Silmarillion, ch 20, pg 193
The Unfinished Tales, Narn i Chîn Húrin, pg 80