Used 20,000-Names.com

Ashleigh only:
Boys
Ali
Ash
Ashe
Eli
Elias*
Giles
Gil
Hal

Girls
Ashlie
Gail
Gia
Haleigh
Lea
Leah
Leigh
Lisa
Shelagh
Sheila
Shelia

Elizabeth only:
Boys
Abe
Abel
Ali
Eli
Hal
Lee

Girls
Abi
Bailee
Bee
Bet
Beth*
Eliza*
Ethel
Hailee
Hazel
Lea
Liz
Liza
Thea
Tia
Zelia


The rest from both:
Boys
Basil
Billie
Ellis
Gabe
Gable
Heath
Leslie
Seth*

Girls
Abigael
Abigail*
Aisha
Aleesha
Alesha
Alethea
Alisha
Alishia
Alisia
Allie
Asha
Ashlee
Asia
Bailie
Bella
Belle
Betsie
Elisabet
Elisabeth*
Ella
Elle
Ellie
Estelle
Gisele
Giselle*
Hallie
Hazelle
Hestia*
Hibah
Isabel*
Isabelle*
Laila
Lilith
Lizie
Salli
Sallie
Sheba
Stella
Zella

Letters I badly need in my name: n, m, c, d, o, y!

*ones I like.