Tharkûn is Gandalf's Dwarvish name, meaning "Gray Man" or "Gray One". Originally, Tolkien translated this as "Staff Man", a reference to Gandalf's wizard staff. However, there were other wizards, and calling him "Grey One" would identify him more uniquely. Tolkien's writings that say "gray" are, as far as I can determine, later sources than those that say "staff". Tharkûn shows the exact same pattern as Nargûn, including being derived from an adjective. Following the example of Narâg, Narag-zâram, and Nargûn, the indefinite, singular form is probably tharâk "gray". It then takes composition form tharak and has the same -ûn "suffix of specificity" as Nargûn, causing the second vowel of the stem to be suppressed.
Because Gandalf is a male being (or at least takes on a male, corporeal form) and the -ûn suffix differs from the -ân and -în of Gabilân and Nuluk-khizdîn, it could be a specifically masculine suffix form. This lines up with the Adunaic affixes -u(-), -û(-), and -ô(-), which are used to derive masculine nouns.
Tharkûn is, most likely, "Gray One" and singular, nominative, definite (proper noun).
The Lord of the Rings, The Two Towers, Book IV, ch 5
The Unfinished Tales, pg 353
Parma Eldalamberon XVII: Words, Phrases and Passages, pg 88