One really could go on, all but infinitely, listing noteworthy composers...depending on how loosely one defines the term "noteworthy." I find myself constantly having to run back and stick people I forgot to mention into the previous lists. Probably, from here on out, I'll just go by the rule of thumb: if I can think of them off the top of my head, the first time through, they're noteworthy. If they come to mind later, that's too bad! So, if you want to find out about Canteloube, Chadwick, and Cui, sorry, you'll just have to W.T.S. yourself!
In that spirit, I give you the "third string" composers whose names begin with D. (Bear in mind, once again, that I am skipping over the really obvious ones that I mentioned here and here.) The interesting thing many of these composers have in common is that you'll never guess how to pronounce their name!
Danzi (Franz) composed loads of well-crafted music, of no particular genius. He is mainly noted today for his woodwind quintets (written for equal parts flute, oboe, clarinet, French horn, and bassoon), of which I have heard a few. They are charming to listen to, though like a lot of chamber music, those who perform them probably best appreciate their charm.
Daquin (Louis-Claude) wrote organ music in the infancy of music's "classical period." Among his most famous pieces are his Noëls (Christmas pieces based on folk carols), some of which I myself have enjoyed playing.
Dargomyzhsky (Alexander) was a 19th-century Russian composer celebrated for writing the most excruciatingly boring opera ever: The Stone Guest (not to be confused with The Stoned Guest, by P. D. Q. Bach). An almost word-for-word setting of an entire play by Pushkin, it was Dargomyzhsky's last effort to demonstrate his theory that "music drama" should be as close to the realism of the spoken word as possible. The effort killed him (the opera was completed after his death by other composers), and its results are still killing audiences, mostly in Russia.
Delibes (Leo) was a late-Romantic, French composer, best remembered for his ballets Coppélia and Sylvia, and for his opera Lakmé, which are still heard (at least in part) today.
Delius (Frederick) was an English-born composer of German extraction, who wrote much of his music in America and France. His first major composition, inspired by his time trying to run his father's orange-growing business, was the Florida Suite. He went on to write highly unusual music gushing with exotic beauty, including cantatas (based on texts by Whitman and Nietzsche, for instance), orchestral works such as Brigg Fair, and one of the first operas to have a black hero.
Diamond (David) was an American composer who wrote numerous symphonies and string quartets (11 each), 3 violin concertos, a "Kaddish" for cello and orchestra, and the popular orchestral piece Rounds.
d'Indy (Vincent) was a French composer and antisemitic jerk who was nevertheless admired in his day as a music educator, scholar, and composer. His best known works today are Istar (a backward set of variations that get simpler and clearer until the theme emerges) and Symphony on a French Mountain Air, written for piano and orchestra.
Ditters von Dittersdorf (Carl), beloved of double-bass players (for whom he wrote two concertos), was a contemporary of Haydn who had a similarly enormous output; for example, 110 symphonies. That is not a typo. I've heard some of Dittersdorf's symphonies and they aren't bad; but they are mainly preserved as a witness to the background against which such giants as Haydn and Mozart worked.
Dohnányi (Ernő, a.k.a. Ernst von) was a Hungarian pianist, conductor, and composer of pretty much Romantic music, even though he lived until 1960. Though he wrote symphonies and concertos galore, his best-known work is the Variations on a Nursery Tune (Twinkle, Twinkle, Little Star), an irreverent parody of other well-known composers, subtitled "For the enjoyment of humorous people and for the annoyance of others."
Donizetti (Gaetano) was one of the leading composers of bel canto opera (along with Bellini), which has lately been growing in popularity after a period of neglect. I actually croaked out a couple of his arias when I was in college; they are extremely challenging, but just as beautiful. His most popular operas include Lucia di Lammermoor, L'elisir d'amore, and Don Pasquale.
Dowland (John) was a seventeenth century lutenist and composer of wistful lute songs, which are quite interesting to hear, if you can get hold of a recording of...well, 17th-century lute songs. His greatest hits include "Flow My Teares" and "Come Again." Though they may not be the stuff of today's Top 40, Dowland's songs have influenced many musicians of this modern age, from Benjamin Britten to Elvis Costello.
In case you thought Dowland a bit dowdy, consider Dufay (Guillaume): a fifteenth-century (!) composer of mainly vocal music, such as masses (some of the first complete musical settings of a mass by a single composer) and both religious and secular part-songs. Dufay was one of the first composers to use a harmonic effect called fauxbourdon, in which whole phrases of melody were accompanied by parallel motion in the other voices. Click the above link to see an example of fauxbourdon from Dufay's music.
Dupré (Marcel) was a virtuoso organist, composer, and music scholar. His best music is not only technically brilliant but powerful and exciting as well. One of my friends played a Dupré piece for a college recital and I was thrilled, as much for my friend's sake (to be able to pull off such a piece!) as by the music itself.
Duruflé (Maurice) was another French organist, teacher, and composer of mostly organ and choral music, though not very much of it. I have probably heard nearly all of his works; but some of it is deeply, deeply special to me. I hope you get a chance to hear some of it; any of it!
Dutilleux (Henri) is yet another French composer, this one still living. His major works include a cello concerto (Tout un Monde Lointain), a violin concerto (L'Arbre des Songes), and thought-provoking orchestral works such as Métaboles. To steal a metaphor from baseball, Dutilleux doesn't come to bat very often, but he seems to be a heavy hitter.