IAU nomenclature:
Baade
Baade, Vallis
Babakin
Babbage
Babcock
Baby Ray (Baby Ray Crater) (Apollo-16 site)
Back
Backlund
Baco
Baillaud
Bailly (Basin)
Bailly-Newton Basin
Baily
Balandin
Balboa
Baldet
Ball
Balmer
Balmer-Kapteyn Basin
Banachiewicz
Bancroft
Banting
Barbier
Barkla
Barlow, Dorsa
Barnard
Barocius
Barringer
Barrow
Bartels
Bawa
Bayer
Beals
Bear Mountain (Apollo-17 site)
Beaumont
Becquerel
Becvár
Beer
Behaim
Beijerinck
Beketov
Béla
Bel'kovich
Bell
Bellinsgauzen
Bellot
Belopol'skiy
Belyaev
Bench (Apollo-12 site)
Benedict
Bergman
Bergstrand
Berkner
Berlage
Bernoulli
Berosus
Berzelius
Bessarion
Bessel
Bettinus
Bhabha
Bianchini
Biela
Bilharz
Billy
Billy, Rima
Bingham
Biot
Birkeland
Birkhoff (Basin)
Birmingham
Birt
Birt, Rima
Bi Sheng
Bjerknes
Black
Blackett
Blagg
Blanc, Mont
Blancanus
Blanchard
Blanchinus
Blazhko-/
Bliss (aka Birt's Jackson-Gwilt)
Block (Apollo-12 site)
Bobillier
Bobone-/
Bode
Bode, Rimae
Boethius
Boguslawsky
Bohnenberger
Bohr
Bohr, Vallis
Bok-/
Boltzmann
Bolyai
Bombelli
Bondarenko
Bonitatis, Lacus
Bonpland
Boole
Boot Hill (A-11 region)
Borda
Borel
Boris
Boris, Rupes
Borman
Born
Borya (Luna-17 site)
Bosch
Boscovich
Boscovich, Rimae
Bose
Boss
Bouguer
Boussingault
Bouvard, Vallis
Bowditch
Bowen
Bowen-Apollo (Apollo-17 site)
Boyle-/
Brackett
Bradley, Mons
Bradley, Rima
Bragg
Brashear
Braude
Brayley
Brayley, Rima
Bredikhin
Breislak
Brenner
Brewster
Brianchon
Bridge (Apollo-15 site)
Bridgman-/
Briggs
Brigitte, Catena
Brisbane
Bronk
Brontë (Apollo-17 site)
Brouwer
Brown
Bruce
Brunner
Buch
Bucher, Dorsum
Buckland, Dorsum
Buffon
Buisson
Bullialdus
Bunsen
Burckhardt
Burckhardt, Rima
Bürg
Bürg, Rimae
Burnet, Dorsa
Burnham
Büsching
Butlerov-/
Buys-Ballot-/
Byrd
Byrgius
Byrgius, Rima

Unofficial nomenclature:
Baby, The (Mons Delisle)
Badvari (the same region as Rand McNally's Andreus hills?)
Baieri (IAU: Delisle)
Baily, Rima (on the floor of Baily)
Baily B, Rimae (SSW of Bailly B)
Baily West, Rima (short broad rille W of Baily)
Baker (one of the triplet of craters NW of Langrenus)
Bakhchivandzhi (Korolev C)
Bakii (IAU: Arago)
Balboa, Rimae (on the floor of Balboa)
Baldet (Cassini E)
Ball, L.F. (Endymion B)
Ballet crater (Apollo-17 site)
BALTHASARIS Hispa. Pri. (IAU: Aristarchus)
Balzac (Hirayama K)
Banat, Cape (Promontorium Banat)
Banat, Sinus (see Banat, Cape)
Banat's snake (immediately north of Prom. Banat)
Banting's Pacman (SE of Banting)
Barange (Marius A)
Barbara Mesa (A-11 region)
Barbarini (IAU: Mosting)
Barcroft (Dollond B)
Barjea (Apollo-17 site)
Barker (Sasserides A)
Barker's Quadrangle (aka Trapezium)
Barlaei (IAU: Atlas A, or Atlas Alpha?)
Baronisus, Mons (IAU: Mairan)
Barreae (IAU: Burckhardt)
Barth (IAU: Grove)
Bartlett (-120/ +900)
Bartolus (Bailly B)
Basaltic Lava Areas (see Vieta)
Basketball player (the Full Moon's dark mare-regions)
Bassett (IAU: Scaliger)
Batavicus, Sinus (IAU: Mare Nectaris and Sinus Asperitatis)
Baudelaire (SE of Xenophon)
Baum (Sven Hedin F or E)
Bazan (IAU: Pytheas)
BBB (see Big Backside Basin)
Beaded ridge (see Wallace)
Beals, Rimae (on the floor of Beals)
Bear Mountain (A-11 region)
Beaumont, Rimae (immediately east of Beaumont)
Beaumont's 29 East ridge / Dorsum Beaumont (North of Beaumont)
Bechleri (IAU: Triesnecker)
Beda (IAU: Censorinus N)
Bedae, S. (IAU: Langrenus B, K, F)
Beer, Catena (aka the LTO's Fossa Archimedes)
Beethoven, Rima (part of Rimae Prinz)
Beetle, The (Birt and Birt A)
Bekii (IAU: Godin)
Bela circularity (circular shape at Bela in Montes Apenninus)
Belgicum, Mare (IAU: Mare Tranquillitatis)
Bel'kovich, Rima (on the floor of Bel'kovich)
Bel'kovich-Hayn shadow (clair-obscur phenomenon, see Bel'kovich)
Belukha, Mons (part of Rupes Altai)
Benavidi (IAU: Gay-Lussac Nu?)
Benitez (Pontanus A or C)
Bennett Hill (see Apollo-15 site)
Bernini (Jansen L)
Berosus, Mons (IAU: Romer)
Bertaud (Sirsalis A)
Bervoeti (IAU: Ramsden)
Besbicus, Insula (IAU: Manilius)
Bessarion D hillock (east of Bessarion D)
Bessel Ray (see Bessel)
Bettinii (IAU: Bessarion and Bessarion A)
Bezout (Mechnikov D)
Biaei (IAU: Hercules)
Bibendum (east of Lansberg)
Bibendum (east of Gassendi, in the Andreus hills)
Bichi (IAU: Riccius)
Bicke, Cape (IAU: south of Mare Crisium)
Bickeri (IAU: Vitello)
Big Backside Basin (the SPA / Southpole-Aitken Basin)
Big Depression (Apollo-16 site)
Bigourdan (location unknown)
Big Rock Mountain (Apollo-15 site)
Big Sag (Apollo-16 site)
Big Sink (Apollo-16 site)
Bird, the (Irregular Mare Patch N°71)
Bird's foot (system of wrinkle ridges on the floor of Wargentin)
Bishop mountains (see Mare Humboldtianum)
Bitterroot meadows (near Apollonius)
Blancani (IAU: Flamsteed Rho, etc.)
Blinky (Apollo-15 site)
Blitterswyckii (IAU: Atlas)
Bluereed meadow (Palus Epidemiarum)
Bob's Bend (A-11 region)
Bode E, Rima (north of Bode E)
Bode Pyroclastics (see Bode)
Bodinus, Mons (IAU: Cepheus and Franklin)
Bohnenberger F, Rimae (northwest of Bohnenberger F)
Boivinii (IAU: Newcomb)
Bojena (location unknown)
Bolton (-103/ -0.88)
Bond, G. (or Bond, G.P., see G. Bond)
Bond, W. (or Bond, W.C., see W. Bond)
Bonestell (Cabeus B)
Bontas, Mons (IAU: Democritus)
Bonvicini (IAU: Riccioli D dark spot)
Boquet (location unknown)
Borbonicum, Mare (IAU: Mare Nubium)
Borealis, Insula (IAU: part of Mare Frigoris)
Borealis, Promontorium (IAU: north of Mare Imbrium)
Boreum Mare (IAU: Mare Frigoris)
Borman (IAU: Pasteur)
Borysthenes, Lacus (IAU: western portion of Lacus Somniorum)
Bosphorus, Sinus Propont. ad. (IAU: NE corner of Mare Vaporum)
Bottle / Guitar (between Fedorov and Mons Delisle)
Bottle (near the SW part of Niepce)
Bouguer B, Rima (ESE of Bouguer B)
Bracamonti (IAU: Polybius)
Bradley, Fossa
Brahei (Tycho) (IAU: Aristoteles)
Brahms, Rima (near Mons Delisle, Delisle, and Diophantus B)
Brand (Danjon X)
Brandy (Apollo-15 site)
Brayley Alpha, Rima (near the hill Brayley Alpha)
Brianchon, Vallis (at the northern part of Brianchon's rim)
Bridge of O'Neill (see O'Neill's bridge, Promontoria Lavinium and Olivium)
Briggi (IAU: Curtius B)
Briggs, Rimae (on the floor of Briggs)
Bright Crater (Apollo-12 site)
Bright eye (Hipparchus C during Full Moon)
Bright one, the (IAU: Necho) (aka NASA's Roosa)
Brittannia (IAU: Mare Crisium)
Broken Ellipse (Irregular Mare Patch NW Jansen G, aka Carrel 1)
Brunii (IAU: Carmichael)
Bucher, Mons (the SSE end of Dorsum Bucher)
Bullialdi (IAU: Reiner Gamma)
Bunsen, Rimae (on the floor of Bunsen)
Burnet, Rima (west of Dorsa Burnet)
Burrell (-809/ -130) (Schmidt's Melloni?)
Buss (-992/ -0.18)
Buster (Apollo-16 site)
Butterfly nut (the western part of Rima Delisle) (aka Dogbone / Winged nut)
Buzz Saw (the opposite of the Jewelled Handle effect at Sinus Iridum and Montes Jura)
Byces, Palus (IAU: Sinus Amoris)
Byrgius A: La Paz (Wilkins)
Byzantium (urbs) (IAU: Menelaus)