Khuzdul / Khuzdûl
The language of the Dwarves in Middle-earth is Khuzdul, which is sometimes spelled Khuzdûl. It was given to them by Aulë, their maker, and they treasure it as a gift from him and a memento of their past, more glorious days. It can be translated simply as "Dwarvish".
The element khuzd- can easily be recognized from this word, meaning "Dwarf". Here it is singular, nominative, composition.
That leaves -ul as a probable suffix. It should correlate to the English suffix -ish in "Dwarvish", making it an adjectival marker. It shows up in Azanulbizar as well as Fundinul, where in both Tolkien refers to -ul as a "genitive ending of patrynomics...". As noted in the discussion on Fundinul, the -ul suffix looks very similar to the Arabic nisba, making it very probable that it is an adjectival suffix.
The only question is why the spelling Khuzdûl shows up. There are only two places that it is seen, at least that we know of. One is in the the essay Of Dwarves and Men, which we read in The Peoples of Middle-earth. The other is in notes that attempt to explain the origin of the word Lhûn. Both of these are late writings, being dated around 1968 or 1969. The name Khuzdûl is used in discussion of other matters, but no explanation is given for the <û>. The form Khuzdul is used everywhere else, including the published stories (The Lord of the Rings and The Silmarilion). It's possible then that Tolkien had some reason for the change. Perhaps the adjectival suffix -ul was a composition form, or only used when a word was used attributively to describe another noun. The -ûl would then be the form seen as a subject or object noun. However, we'll probably never know, unless there is some indication in yet unpublished works. In any event, vowels are somewhat variable when it comes to derivation in Arabic (and perhaps other Semitic languages). There isn't one, absolutely set vowel pattern used for a given function. We can therefore simply view the form Khuzdûl for what it is: a variant form that most likely doesn't have many implications.
I will say that Khuzdul (or Khuzdûl) is singular, nominative, definite (proper noun), and means "Dwarvish".
The Peoples of Middle-earth, pg 297, 300, 316-317, 321-323, 358
The War of the Jewels, pg 205
Vinyar Tengwar, Volume 5B, issue 48, pg 24