Ok these names would do for rabbits & rodents.
Everyday pet names:
Female
Basil
Binky
Angel
Butterscotch
Buttons
Cleo
Crystal
Dakota
Cutie Pie
Dolly
Ebony
Fifi
Fluffy
Flopsy
Ginger
Gucci
Hazel
Misty
Jilly
Lady
Lilly
Lola
Lucy
Millie
Molly
Muffin
Peaches
Pinky
Princess
Rosie
Roxy
Sadie
Savanah
Sassy
ShnuggleBunny
Shadow
Snowy
Snow Flake
Snow ball
Sprinkles
Sweetie
Vanilla
Willow
Oreo
Sugar
Male
Alfie
Baggins
Bandit
Bingo
Biscotti
Blackie (male or female)
Buster
Chester
Daffy
Danny
Diego
Elmo
Fudge
Harley
Henry
Houdini
Jake(y)
Jelly Bean
Joker
Joey
Kirby
Kobi
Nugget
Oscar
Oreo
Rascal
Simba
Smokey
Thumper
Tazz
Tigger
Zeus
Unique names
The shelter may not want to use more unique names because they might be hard for people to pronounce or they want more cute, everyday names but I thought I'd stick them in anyway
Male Irish names
Aidan
Oran
Liam
Fionn
Brendan
BrÃn (bree-ann)
Cian
Cillian (kill-ian)
Eamon
Emmet
Felim (fail-im)
Malachi (like this one, mah-lah-key)
Ultán (ult-un)
Female Irish Names
Briana
Bronagh (bro-nah)
Cara (Car-ah)
Ciara (Key-Rah)
Erin (air-in)
Ina (e-nah)
Shakespearean Names:
Male:
Alonso
Romeo
Hamlet
Arthur
Benvolio
Cassio
Charles
Christopher
Dion
Duncan
Francisco
Dion
Hugh
Marcus
Malcolm
Oliver
Paris
Toby
Female
Ophelia
Juliet
Beatrice
Diana
Emilia
Regan
Silvia
Titania
Viola
Twilight:
Bella
Edward
Carlisle
Alice
Rosalie
Emmett
Jasper
Esme
Renesmee
Jacob
Sam
Leah
Seth
Embry
Quil
Paul
Felix
Heidi
Jane
Demetri
Renata
Victoria
Hope I helped some bit, and there are some decent names in there