C nomenclature (from the IAU and from unofficial sources)

Italics indicate farside features.

An additional list of names for Clair-Obscur phenomena on the moon's morning and evening terminator:
http://the-moon.wikispaces.com/clair-obscur

Note:
Johann Hewelcke's name Mons Mampsarus is a typographical error. On his chart it is Mons Campsarus.
IAU nomenclature
C. Herschel (Caroline Herschel)
C. Mayer (Christian Mayer)
Cabannes
Cabeus
Cai Lun
Cailleux
Cajal
Cajori
Calippus
Calippus, Rima
Camelot (Apollo-17 site)
Cameron
Campanus
Campbell
Cannizzaro
Cannon
Cantor
Capella
Capella, Vallis
Capuanus
Cardanus
Cardanus, Rima
Carlini
Carlos
Carmen, Rima
Carmichael
Carnot
Carol
Carpatus, Montes
Carpenter
Carrel
Carrillo
Carrington
Cartan
Carver
Casatus
Cassegrain
Cassini
Catalán
Catharina
Cato, Dorsa
Caucasus, Montes
Cauchy
Cauchy, Rima (aka Fossa Cauchy)(-LTO-)
Cauchy Fault (Rupes Cauchy)(aka Fossa Casals)(-LTO-)
Cavalerius
Cavendish
Caventou
Cayeux, Dorsum
Cayley
Cayley Formation
Celsius
Censorinus
Cepheus
Ceraski (see Tseraskiy)
Chacornac
Chacornac, Rimae
Chadwick
Chaffee
Challis
Chalonge
Chamberlin
Champollion
Chandler (and nearby highland ponds)
Chang Heng
Chang-Ngo
Chant
Chaplygin
Chapman
Chappe
Chappell
Charles
Charlier
Chaucer
Chauvenet
Chawla
Chebyshev-/
Chernyshev
Chevallier
Ching-Te
Chladni
Chrétien
Christel, Vallis
Cichus
Cinco (Apollo-16 site)
Clairaut
Clark
Clausius
Clavius
Cleomedes
Cleomedes, Rimae
Cleopatra, Rima
Cleostratus
Clerke
Cloos, Dorsum-/
Coblentz-/
Cochise (Apollo-17 site)
Cockcroft-/
Cognitum, Mare
Collins
Colombo
Compton (Basin)-/
Comrie
Comstock
Concordiae, Sinus
Condon
Condorcet
Cone (Apollo-14 site)
Congreve
Conon
Conon, Rima
Cook
Cooper-/
Copernicus (aka Monarch-of-the-Moon)
Cordillera, Montes
Cori
Coriolis-/
Couder
Coulomb (Zdenek Kopal's Nechville)
Coulomb-Sarton Basin
Courtney
Cremona-/
Crescent (Apollo-12 site)
Crile
Mare Crisium (Basin)
Crocco
Crommelin-/
Crookes-/
Crozier
Crüger
Ctesibius-/
Curie-/
Curtis
Curtius
Cusanus
Cushman, Dorsum
Cuvier
Cyrano
Cyrillus
Cysatus
Unofficial nomenclature
Caloris, Terra
Cape, the (A-11 region)
Cape Bruce (A-11 region)
Cape Venus (A-11 region)
Cadmus, Mons (IAU: Parrot C) (Wilkins's Millas, Lamech's Muller)
Caes, Facula (the high-albedo craterlet NW of Sinus Honoris)
Caes, Mons (see Helmholtz)
Caesar, Julius (see Julius Caesar)
Calabraria, Insulae (IAU: probably parts of Montes Teneriffe)
Calathe, Insula (IAU: Tobias Mayer Beta, Rho, etc.)
Calchistan, Mons (IAU: Maurolycus, Stofler, etc.)
Caleni (IAU: Asclepi)
Calippi, Promontorium (Rukl: 48)
Cambierii (IAU: Sabine)
Camoens (south of Schubert C)
Campanus, Rima (on the floor of Campanus)
Campsarus, Mons (bright area at Suess)
Candide (Apollo-17 site)
Canoe (Apollo-16 site)
Cantelmi (IAU: Cichus)
Canyon (Apollo-15 site)
Cape Plato (see Plato)
Capraria, Insula (IAU: Montes Teneriffe Epsilon)
Caramuel (IAU: Bartels)
Caramuelis (IAU: Descartes C / Dollond E)
Carcinites, Sinus (IAU: the eastern portion of Lacus Somniorum)
Caroli D. Loth. (IAU: Metius)
Caroli D. Mant. (IAU: Jacobi)
CAROLI I Reg. Britt. (IAU: Walther)
Carpates, Mons (IAU: Eudoxus)
Carpathian plateau (see Copernicus)
Carpathos, Insula (IAU: Max Wolf)
Carr (IAU: Perepelkin)
Carrel 1 (Irregular Mare Patch NW of Jansen G) (aka the Broken Ellipse)
Cartesii (IAU: Romer)
Carthusia (IAU: Copernicus)
Cayley zone (see Descartes)
Caruso, Fossa (SE of Nielsen)
Casals, Fossa (Rupes Cauchy)
Casimiri Pol. P. (IAU: Mutus)
Casius, Mons (1) (IAU: Fourier and Vieta)
Casius, Mons (2) (IAU: Agatharchides P) (Wilkins's Novellas)
Caspia (IAU: Mare Crisium)
Caspium, Mare (De Moura) (IAU: Mare Crisium)
Caspium, Mare (IAU: Mare Fecunditatis)
Cassegrain, Mons (WNW of Cassegrain)
Cassini C, Rima (NW of Cassini C)
Cassini M, Rima (N of Cassini M)
Cassini's Bright Spot (unofficial name for Hell Q)
Cassini's moon maiden (see Promontorium Heraclides)
Cassiodori, Promontorium (Rukl: 48)
Cassiotis regio (IAU: the eastern border of Mare Humorum)
CAT (Charles And Tom) (Apollo-16 site)
Cataractes, Mons (IAU: Gassendi)
Catholicum, Fretum (IAU: Mare Vaporum and Sinus Aestuum)
Cat's Paw (Apollo-11 site)
Caucasius, Sinus (IAU: Sinus Concordiae)
Caucasus Inferior, Montes (IAU: Borda, Santbech, etc.)
Cauchy D hills (NNE of Cauchy D, in W part of Sinus Concordiae)
Cauchy-5 (field of Irregular Mare Patches west of Donna in Mare Tranquillitatis)
Cauchy, Fossa (Rima Cauchy)
Causeway (Bullialdus W)
Cavalerius B, Rima (on the floor of Cavalerius B)
Cavalerius D, Rima (on the floor of Cavalerius D)
Cavendish, Rima (on the floor of Cavendish)
Cavendish, Rimae (I and II) (southeast of Cavendish)
Cayley's mob (cratercluster between Cayley and Rima Ariadaeus)
Cayley Plains (see Cayley Formation)
CBVC (see Compton-Belkovich Volcanic Complex)
Celenorum Tumulus (IAU: the chain La Caille to Vogel)
Cellini (Kastner S)
Cercinna, Insula (IAU: Kepler's bright nimbus)
Cerda (IAU: Krieger)
Cervantes (Wyld J)
Cesaris, Promontorium (Rukl: 47)
Chacornac, Fossa
Chadisia, Promontorium (IAU: somewhere near Moltke)
Chaffee (IAU: Subbotin)
Chain (Apollo-15 site)
Chain Gulch (A-11 region)
Chajorra (see Teneriffe, Montes)
Chalcidici, Montes (ejecta-ray east from Copernicus)
Chama Peak (A-11 region)
Chamisso, Cap (IAU: Mons Argaeus)
Chandler's highland ponds (see Chandler)
Chapman D, Vallis (valley at Chapman D)
Chappell, Rimae (on the floor of Chappell)
Chappy (ray-craterlet on Chaplygin's rim, see Chaplygin)
Charlesworth (IAU: Saha)
Cheerio crater ("ghost"-crater near Angstrom)
Chekov (Kastner R)
Chenier (Patsaev Q)
Chigi (IAU: Tacitus)
Chisletti (IAU: Lambert)
Chopin, Rima (very near Montes Agricola)
Chopper, The (the chopper-shaped cratercluster at La Hire C)
Christi, Mons (IAU: Mons Piton)
CHRISTIERNI IV Reg. Daniae (IAU: Purbach)
CHRISTINAE Reg. Suec. (IAU: Regiomontanus)
Chuck Hole (A-11 region)
Ciermanni (IAU: Brayley)
Cilicum, Insula (IAU: Arago)
Cimaeus, Mons (IAU: Halley and Hind)
Cimmeriae, Paludes (IAU: Lacus Bonitatis, etc.)
Cimmerius, Mons (IAU: Macrobius)
Cinder Cone (dark craterlet near Lassell C, see Lassell)
Circaeum, Promontorium (IAU: somewhere near Timocharis)
Circle harbour (Luna-21 / Lunokhod 2 site)
Cirna, Mons (location unknown)
Cisneutra (see Riphaeus, Montes)
Cissemlja (see Riphaeus, Montes)
Clarae Isab. Leop. F. (IAU: Sulpicius Gallus M bright spot)
Claramontii (IAU: Bianchini)
Clark / Clark-Apollo (Apollo-17 site)
Clarkson (Gassendi A)
Clavii (IAU: Promontorium Laplace)
Claw, the (Irregular Mare Patch N°22)
Cleomedis, Promontorium (Rukl: 6)
Cleostratus, Vallis (valley WSW of Cleostratus)
Cliff (Apollo-15 site)
Climax, Mons (IAU: Sirsalis, Sirsalis A, and bright nimbus)
Cloverleaf (cratercluster in Aitken)
Cloverleaf (Apollo-14 site)
Cluster mountain (Mons Vinogradov)
Cobavi (IAU: Pico)
Cobra Head (the "source" of Vallis Schroteri)
Cocci (IAU: Vitruvius)
Coci (IAU: Montes Teneriffe Delta, etc.)
Coibacarani, Montes (IAU: Brenner, Fabricius, Metius)
Colchis (regio) (IAU: east of Sinus Asperitatis)
Collins (IAU: Hirayama)
Colombi, Promontorium (IAU: Agatharchides?)
Comas Sola (-760/ -548) (H.Hill's Basaltic Lava Areas?)
Compton peak (central peak of Compton)
Compton-Belkovich Volcanic Complex (CBVC)
Compton, Rimae (on the floor of Compton)
Conde Prin. (IAU: Nasireddin)
Confucius (IAU: Paschen)
Conradi (IAU: Wrottesley)
Constellation of four (Taruntius G, H, K, and P in Mare Fecunditatis)
Contact (Apollo-15 site)
Contarini (probably the Helmet)
Conti (IAU: Tobias Mayer Alpha)
Contour (Apollo-15 site)
Cooke (Eimmart C)
Copernici (IAU: Eudoxus)
Corax, Montes (IAU: Proclus and SW part of rim Mare Crisium)
Cori, Vallis (valley NNW of Cori)
Cornaro (probably the Andreus hills)
Corneille (west of Chauvenet)
Corocondametis, Lacus (IAU: Palus Somni)
Corsica, Insula (IAU: Timocharis)
Cortes (IAU: Demonax A)
Cosyra, Insula (IAU: Tobias Mayer A bright nimbus)
Cove (Apollo-16 site)
Coxwell mountains (SW part of rim Mare Crisium)
Crackled Hills (Apollo-15 site)
Cragus, Mons (IAU: Arzachel)
Crani (IAU: Delambre)
Cratas, Mons (ejecta-ray north of Copernicus)
Crater chain (Stadius craterlets)
Crathis, Mons (IAU: Fra Mauro Kappa, Gamma, Zeta)
Crequii (IAU: Airy)
Crescent (Apollo-15 site)
Creta, Insula (IAU: Bullialdus)
Creticum, Mare (IAU: probably near Bullialdus)
Croii (IAU: Heraclitus and Licetus)
Crook (Apollo-15 site)
Crookes X, Catena
Crossroads (Apollo-14 site)
Crown (Apollo-16 site)
Crugeri (IAU: Promontorium Heraclides?)
Crystal (Apollo-15 site)
Cuevio (IAU: Montes Harbinger Alpha)
Curtii (IAU: Furnerius?)
Curtiss Cross (clair-obscur phenomenon at Fra Mauro Zeta, see Fra Mauro)
Cusae (IAU: Eudoxus Kappa)
Cyanea Europa, Insula (IAU: vague bright area north of Tacquet)
Cydises, Mons (IAU: Apianus)
Cyprus, Insula (IAU: Birt)
Cyrillus, Cap (IAU: Promontorium Agarum)