This is seen in the inscription on Balin's Tomb in the Chamber of Mazarbul, which is:


Uzbad Khazad-dûmu

Gandalf read this to the Fellowship and translated Fundinul as "Son of Fundin".  This is usually the English translation used, and even Tolkien employs it.  However, it should be noted that this isn't a word-for-word translation.  Tolkien also provides an explanation of the -ul suffix, saying it "is apparently an adj. or genitive ending here used as a patronymic."  So, -ul does not literally mean "son".  Instead, it turns the name Fundin into an adjective to use as a descriptor for Balin.  A more literal translation might actually be something like "Balin Fundinish", using the -ish suffix of English.  To strike a middle ground, I would offer the translation as "Balin Fundinson".  That would actually match well with patronymics found in Nordic countries, which are the source of the Dwarvish "outer names".

For those unfamiliar with patronymics, they are part of a person's full name.  There are cultures where they were used extensively in the past or still are.  In some cultures, current "last names" or "family names" are derived originally from a patronymic.  Just look at Wilson in English.  Semitic cultures commonly employ patronymics, which makes their use in Khuzdul more expected.  Examples there would be names that include ben- or bat- in Hebrew and ibn, bin, or bint in Arabic.  There are cultures that use adjectival forms of a parent's name as a patronymmic, as is apparently the case in Khuzdul.

As mentioned in the section on Duban Azanulbizar, the -ul suffix seems to be more of a derivational, adjectival morpheme than a genitive noun case.  It matches the Arabic "nisba" suffix -iyy, which is used to form adjectives from nouns and can also be seen in Arabic names.  The line between "genitive" and "adjectival" can be a bit hazy.  However, as stated, words that use this suffix seem to be able to be used in isolation - with the suffix - such as in Khuzdul or Mazarbul.  If this were a true, genitive case ending it would be paired with another noun which would be the object being modified.  As we saw in Baruk Khazâd!, that construction mimics the Semitic construct state quite closely, so that should be considered the workhorse for genitive "X of Y" constructions.  There are probably some different morphological rules in place for a construct phrase like Baruk Khazâd! versus one that uses a word ending in -ul.  Since -ul is probably an adjectival ending, there are most likely requirements for the adjective to match the head noun (the noun being described) in terms of number, definiteness, case, etc.  That would not be true for a construct phrase.

On a final note, the name Fundin is actually somewhat absurd here.  It is not a Khuzdul word or name, and actually is not even a true "outer name" used by Dwarves, since Tolkien used names found in Scandinavian myths to represent the actual names from those cultures.  It was a decision made so as to not overwhelm readers with culturally accurate names, which he feared would make readers less able to relate to the stories.  That said, it would have also been odd for Tolkien to have rendered the actual name, since it would be the only place it was seen, as Fundin would be used elsewhere.

Fundinul is then an adjectival patronym of Balin, roughly meaning "son of Fundin" or "Fundinson" and is singular, nominative, definite (proper noun).

The Lord of the Rings: A Reader's Companion, pg 269
The Treason of Isengard, pg 186, 457
Parma Eldalamberon XVII: Words, Phrases and Passages, pg 47