1 syllable Names

Ann
Ayn
Bay
Bess
Beth
Bette
Blair
Brekke
Brett
Brooke
Cam
Cass
Dale
Day
Elle
Eire
Em
Eve
Fay
Gaye
Gem
Jan
Jane
Jay
Jean
Jen
Jet
Jo
Joan
June
Kat
Kate
Kay
Kit
Lane
Leigh
Liv
Lou
Lynn
Madge
Maeve
Mags
May
Meg
Midge
Moon
Moss
Nan
Nat
Nell
Neve
Noor
Pam
Pat
Pearl
Peg
Pet
Rae
Rain
Rose
Rue
Ruth
Skye
Soon
Sue
Suk
Tess
Ti
True
Truth
Val
Vale
Viv
Ya
Zee

Abe
Al
Ames
Ang
Ashe
Beau (or Bo)
Ben
Bert
Blaine
Blair
Blaise
Bob
Bram
Bran
Brandt
Brent
Brett
Brock
Brook
Brooks
Burke
Burl
Cab
Cal
Cam
Charles
Chance
Chase
Chet
Chuck
Dale
Dan
Dane
Dar
Dave
Dick
Dodge
Dwight
Ed
Fields
Fitz
Ford
Frank
Franz
Fred
Fritz
Gad
Gage
Gray
Guy
Hal
Han
Hank
Hans
Hayes
Hugh
Ike
Jack
Jake
Jan (pronounced "yawn", Scandinavian)
Jarl (pronounced 'yarl', Scandinavian)
Jay
Jed
Jens
Jet
Jim
Jin
Joe
Joel
John
Kale
Kay
Kev
Kit
Lance
Lane
Lars
Lee
Les
Lex
Lorne
Lot
Lou
Lynn
Mack
Mance
Mark
Matt
Max
Mel
Mick
Mike
Miles
Mitch
Nat
Nate
Ned
Nels
Nick
Oak
Oakes
Oh
Oz
Pan
Pat
Paul
Pete
Phil
Rance
Rand
Ray
Reid
Rich
Rick
Rob
Rock
Rod
Roy
Royce
Russ
Sam
Saul
Shaq
Shem
Sky
Steve
Stig
Sven
Tad
Ted
Thad
Thayne
Thor
Thorne
Tig
Tim
Tom
Trent
Trey
Troy
Vance
Vaughan
Vick
Vince
Wade
Walt
Wayne
Wes
Will
Yul
Yves
Zach
Zan
Zane
Zeb
Zed
Zeke

Every Name There Is - B

Here are the girl B names:

Babette

Babs

Bailey

Bambi

Barb

Barbara

Barbarella

Barbarelle

Barbaretta

Barbarette

Barbie

Basia

Bay

Bayard

Beatrice

Beatrisa

Beatrix

Beatriz

Beautiful

Becky

Bedinger

Belen

Bella

Belladonna

Belle

Belphoebe

Benin

Berengaria

Berenice

Beret

Berlin

Bernarda

Bernarde

Bernadetta

Bernadette

Bernadina

Bernadine

Bernardina

Bernardine

Bernardita

Bernestine

Bernetta

Bernie

Bernice

Bernina

Bernine

Berta

Berte

Berthe

Bertha

Bertille

Bertina

Bertine

Beryl

Bess

Bessie

Beth

Bethan

Bethaney

Bethel

Bethia

Bethlehem

Bethzabeth

Betsy

Bettany

Bette

Bettina
Bettine

Betty

Beulah

Bev

Beverly

Bianca

Bienvenida

Bindi

Bitsy

Blakeley

Blanca

Blanche

Blanchefleur

Bliss

Blodwen

Blossom

Bluebell

Blythe

Bo

Bobbetta

Bobette

Bonneville

Bonnie

Boston

Bountiful

Brandilyn

Branwen

Brantley

Breeanne

Brenda

Brendalyn

Brenna

Briallen

Brianda

Bridget

Brietta

Brigida

Brigitta

Brigitte

Briony

Brisa

Brita

Britta

Brittan

Brittanica

Brittney

Bronislava

Bronislawa

Bronwen

Brooke

Brookeleigh

Brooklyn

Brynley

Brynn

Brynna

Buffy

Bunny

And the Boy B Names:

Baldric

Baldwin

Balfour

Bannon

Barclay

Barnabas

Barnaby

Barney

Baron

Barrabas

Barrett

Barry

Bart

Barthelemy

Bartholomew

Bartolo

Barton

Bartley

Bastian

Baxter

Beauregard

Bede

Bedivere

Ben

Benedict

Benjamin

Bennett

Benny

Beowulf

Bernard

Bernie

Bert

Bertrand

Bev

Beverley

Birch

Bjorn

Blaise

Blake

Bo

Boyd

Brad

Bradley

Bram

Brandt

Branwell

Braulio

Brent

Brett

Brian

Brice

Britton

Broderick

Brody

Brooks

Bruce

Bryant

Bryson

Buck

Burke

Burnell

Burton

Byron 

If you know of any I've forgotten, please suggest it in the comments!