A few composers & musicians connected with organism names:
(Likely several more persons connected to music may be found in eponyms, but so far the compiler have only found a few. He must admit, that searching for such persons, have not been intense, but when trying to find eponym names for a few widely liked recent or close to recent musicians or singers, like Alfred Schnittke, 1934-98, Kiri Te Kenawa, 1944-, Om Kalthoum, 1898-1975, and some others, it did not result in any hits)
Hugo Alfven, 1872-1960, Swedish composer [Alfvenia Larsson,1984 (Microspora, cyclopid -however limnic - host)]
The Beatles, well-known British musicians [Bushiella (Jugaria) beatlesi Rzhavsky, 1993 (Annelida, Spirorbidae)]. Presumably also the nematode Greeffiella beatlei Lorenzen, 1969 is named for this group (the author does not explain the etymology, but considering the shaggyness of the worm the analogy with the Beatles haircut is striking). There are also some trilobites named Avalanchurus lennoni, Avalanchurus starri & Struszia mccartneyi, Edgecombe & Chatterton, 1993 and some of their rivals are honored in som other trilobites : Aegrotocatellus jaggeri & Perirehaedulus richardsi Adrain & Edgecombe, 1995. Even members in later popular music groups (Sex Pistols & The Ramones) are honoured in several trilobite names by Adrain & Edgecombe, 1997.
Ludwig van Beethoven, 1770-1827, well-known Dutch-German composer and free-thinker., who left Catholicism for a Pantheism of the kind the poet and natural philosopher Goethe was a spokesman [Gnathia beethoveni Paul & Menzies 1971]
Franz Adolf Berwald, 1796-1868, German-Swedish composer [Berwaldia Larsson, 1981 (Microspora, host Daphnia)].
Farokh (also spelled Farrokh or Farouk) Bulsara (better known as Freddy Mercury in the rock band Queen), (5 Sep.) 1946-91 (24 Nov.), "arguably Zanzibar's most famous popular musician and singer", is honoured in the East African isopod name Cirolana mercuryi N Bruce, 2004. (Dr. Niel Bruce, the author of the name kindly provided the information).
Dietrich Buxtehude, 1637-1707, Danish-German composer born in Hälsingborg (Sweden), where he worked as an organist before he moved to Lübeck [Buxtehudea R. Larsson, 1980 (Microspora, host Petrobius)]
Mercury : (see Bulsara)
Wolfgang Amadeus Mozart, 1756-91, well-known Austrian composer [Bishopina mozarti Bonaduce, Masoli & Pugliese, 1978 (Ostracoda), Mozartiella A. Giangrande, 2005? (nomen nudum - not yet published) (Polychaeta)]. (The wasp name Mozartella beethoveni is of course not appropriate in a marine site, like this) (Dr. Ferdinando Boero kindly provided the polychaete name).
The gastropod name Cymbiola rossiniana (Bernardi, 1859) is honouring Gioacchino Rossini, (29 Feb. - Pesaro) 1792-1868 (13 Nov. - Passy), "to the illustrious composer Rossini, as a tribute of our admiration" in Bernardi's own - but translated - words.
Alfred Éric Leslie Satie (17 May - Honfleur, Normandie) 18866-1925 (1 July - Paris), has possibly no organism names honouring him, but was very influenced by nature and likely knew some french naturalists, because several of his piano compositions have names associating them with marine organisms, e.g. Edriophthalma, Podophthalma & d'Holothurie.
Frank Vincent Zappa, (10 Dec. - Baltimore) 1940-93 (4 Dec. - Los Angeles), well-known US composer & musician [Zappa Murdy, 1989 (Gobiidae), Phialella zappai Boero, 1987 (Leptomedusa)]. The author of the hydromedusa name, the Italian zoologist (Ferdi)Nando Boero was repayed with the song "Lonesome Cowboy Nando" in "You Can't Do That On Stage Any More, Vol.6" by Zappa. Also the fossil gastropod Amaurotoma zappa Plas, 1972 and spider Pachygnatha zappa Bosmans and Bosselaers, 1994 are named for him and the The ZapA gene in the bacterium Proteus mirabilis was named so in 1995 in his honour by Bob Belas, Christopher Wassif and Diana Cheek. An asteroid (minor planet), Zappafrank (3834), has also been named in his honour. (Dr. Claudia Mills kindly provided some of this information and also the following link, but Dr. Nando Boero kindly corrected the first name to Frank (and not Francis, which is the name of his father))
N.B. Not only professional musicians and composers is involved in music. Several important invertebrate workers did also conduct music or was at least much interested. Some of these were: J.-B. Lamarck (started to study violincello playing during his first years in Paris), Comte de Lacépède (composing symphonies and operas), G.O. Sars (played flute in young years and the Hardanger fiddle during excursions - like a common violin, but built in thinner wood and with 4 (or 5) extra strings below the four ordinary strings, which resonate under influence of the normal strings; himself admitting that if he had not been a zoologist, he would prefer to be a musician), O.F. Müller (studied music during his youth in Copenhagen, but did only use these skills as a music teacher, but it is said that he and his wife - who turned out to be a music lover as well - met by a small Norwegian organ, likely when he played upon it; his father Nikolaj was a court trumpeter), E. Heron-Allen (this friend of the family of Oscar Wilde knew everything about the violin, violin building and playing) W.H. Leigh-Sharpe (wrote classical piano compositions), S.L. Lovén (was an interested musician and founded a concert song society when still in Lund), G.W. Tryon Jr. (music composer & publisher), L.G. Hertlein (beside fossil shells also very interested in music, theater, literature and football), J.S. Garth (started his career as a musician, but changed career to become a crab and butterfly specialist), C.T. Crocker (when not devoting himself to oceanic expeditions, he mainly wrote librettos for the opera and other musical events), H.J. Finlay (liked very much operas by Bizet, Verdi & Wagner and composed music as well as playing the piano himself), J.G. Dalyell (published i.a. on music from Scotland) and certain persons were either collectors of music instruments like F. Stearns or relatives or friends of composers, like K.I. Skrjabin (relative of A.N. Skrjabin) & E. Fauré-Fremiet (son of Gabriel Fauré, himself a disciple of Saint-Saëns), M.N. Rimsky-Korsakov (N.A. Rimsky-Korsakov's son), E.G. Racovitza (all his family was very interested in music & poetry). See also C.E. Mills, who sometimes have conducted chamber music together with colleagues like G. Mackie, M. Strathmann & E. Kozloff.