I just can’t find anything that says this is it! I try to stay away from popular and trendy. I also really love E names for girls. This is what I have so far:
[name_u]Eden[/name_u]
[name_f]Adaline[/name_f]
[name_f]Eloise[/name_f]
[name_u]Everly[/name_u] (trendy?)
[name_f]Anneliese[/name_f]
[name_f]Noelle[/name_f] (but it’s my cousins name)
I love the name Eden! and I don’t think Everly is too trendy at all! I also really like Adaline and Anneliese. I LOVE the name Noelle. If you dont want to use it as a first name since it’s your cousins, you could use it as a Middle! ex: Everly Noelle, Eden Noelle, Anneliese Noelle etc.
Other E names I like are
Ebony
Echo
Elena
Elsie
Elliot
Ember
Emberly
Embry
I hope these suggestions help and aren’t too popular or trendy for you. I tried to get a little of everything in there. 
You have a very similar style to me and I adore all your names. I also agree it may be best to put [name_f]Noelle[/name_f] as a middle because of it being your cousin’s name. I think my favorites would be [name_f]Anneliese[/name_f] and [name_u]Everly[/name_u]!
I love [name_f]Anneliese[/name_f] and [name_u]Eden[/name_u]! [name_m]How[/name_m] about [name_f]Noella[/name_f] nn [name_f]Ella[/name_f]?
[name_f]Evelina[/name_f]
[name_f]Eliana[/name_f]
[name_f]Evelyne[/name_f]
[name_u]Emerson[/name_u]
[name_f]Evangeline[/name_f]
Emmelynn
These are all very nice.
[name_u]Eden[/name_u] is a great name! I like [name_f]Anneliese[/name_f] and [name_f]Adaline[/name_f], although I much prefer the spelling [name_f]Adeline[/name_f]. [name_u]Everly[/name_u] is a beautiful name, but I would advise against using it if you want to avoid trendy names.
Some E names I would suggest are…
[name_f]Eve[/name_f]/[name_f]Eva[/name_f]
[name_u]Evelyn[/name_u]
[name_f]Evangeline[/name_f]
[name_f]Evaline[/name_f]
[name_f]Esme[/name_f]
[name_f]Emmeline[/name_f]
[name_f]Eleanor[/name_f]
[name_f]Elodie[/name_f]
Other names not starting with E
[name_f]Adelaide[/name_f]
[name_f]Lila[/name_f]
[name_f]Juliet[/name_f]
[name_f]Clementine[/name_f]
[name_f]Cora[/name_f]
[name_f]Isla[/name_f]
[name_f]Alice[/name_f]
[name_f]Matilda[/name_f]
[name_f]Cecily[/name_f]
[name_f]Audrey[/name_f]
[name_f]Olive[/name_f]
Your list is very similar to mine. I have [name_u]Eden[/name_u], [name_u]Everly[/name_u] and [name_f]Annalise[/name_f].
What about [name_f]Clara[/name_f], [name_f]Amity[/name_f], [name_f]Linnea[/name_f]?
[name_u]Eden[/name_u] is a lovely name.
[name_f]Noelle[/name_f]- I wold only use it as a 2nd. I like babies to have their own names.
Most names I would suggest are the same as @stevojeano.
[name_f]Eleni[/name_f]
[name_u]Elliot[/name_u]
[name_u]Ember[/name_u]
[name_f]Elinore[/name_f]
[name_f]Elodie[/name_f]
[name_f]Evadne[/name_f]
[name_f]Evanna[/name_f]
Eleska
[name_f]Elke[/name_f]
[name_f]Erin[/name_f]
[name_f]Elin[/name_f]
[name_f]Ebony[/name_f]
[name_f]Emma[/name_f]
[name_f]Eirene[/name_f]
[name_f]Elle[/name_f]/a short for [name_f]Gabrielle[/name_f]/a
[name_f]Evonne[/name_f]
Best wishes
[name_f]Eva[/name_f]
[name_f]Essa[/name_f]
[name_f]Emmaline[/name_f]
[name_f]Elena[/name_f]
[name_f]Eliana[/name_f]
[name_f]Elise[/name_f]
[name_f]Elora[/name_f]
[name_f]Etta[/name_f]
[name_f]Eve[/name_f]
[name_u]Eden[/name_u]
[name_f]Esther[/name_f]
[name_f]Enid[/name_f]
[name_f]Eris[/name_f]
[name_u]Ellery[/name_u]
[name_u]Emery[/name_u]
[name_f]Elisabeth[/name_f]
[name_f]Elisa[/name_f]
[name_f]Elsie[/name_f]
[name_f]Elsa[/name_f]
[name_f]Ella[/name_f]
[name_f]Ellie[/name_f]
[name_f]Elin[/name_f]
[name_f]Ava[/name_f]
[name_f]Adalie[/name_f]
[name_f]Asha[/name_f]
[name_f]Annora[/name_f]
[name_f]Arabella[/name_f]
[name_f]Aster[/name_f]
[name_u]Aspen[/name_u]
[name_f]Afton[/name_f]
[name_u]Auden[/name_u]
[name_u]Arden[/name_u]
[name_f]Brynn[/name_f]
[name_f]Britta[/name_f]
[name_m]Breck[/name_m]
[name_f]Bella[/name_f]
[name_u]Bevin[/name_u]
[name_f]Cassia[/name_f]
[name_f]Calla[/name_f]
[name_f]Callie[/name_f]
[name_f]Cassandra[/name_f]
[name_f]Calliope[/name_f]
[name_f]Calista[/name_f]
[name_f]Candice[/name_f]
[name_f]Carissa[/name_f]
[name_f]Clarissa[/name_f]
[name_f]Claire[/name_f]
[name_f]Chloe[/name_f]
[name_f]Clover[/name_f]
[name_f]Clarice[/name_f]
[name_f]Delilah[/name_f]
[name_f]Delia[/name_f]
[name_f]Davina[/name_f]
[name_f]Darina[/name_f]
[name_f]Dinah[/name_f]
[name_f]Danica[/name_f]
[name_f]Felicity[/name_f]
[name_f]Fleur[/name_f]
[name_f]Flora[/name_f]
[name_f]Freya[/name_f]
[name_f]Fiona[/name_f]
[name_f]Felicia[/name_f]
[name_f]Faye[/name_f]
[name_f]Gretchen[/name_f]
[name_f]Georgina[/name_f]
[name_f]Hannah[/name_f]
[name_f]Hope[/name_f]
[name_u]Harley[/name_u]
[name_f]Hailey[/name_f]
[name_f]Hester[/name_f]
[name_u]Haven[/name_u]
[name_f]Honor[/name_f]
[name_f]Isabelle[/name_f]
[name_f]Isabella[/name_f]
[name_f]Isaura[/name_f]
[name_f]Ina[/name_f]
[name_f]Ivy[/name_f]
[name_f]Iris[/name_f]
[name_u]Juniper[/name_u]
[name_f]Jane[/name_f]
[name_u]June[/name_u]
[name_f]Jessa[/name_f]
[name_f]Jessamine[/name_f]
[name_f]Jacinda[/name_f]
[name_f]Julia[/name_f]
[name_f]Juliet[/name_f]
[name_f]Katherine[/name_f]
[name_f]Kate[/name_f]
[name_f]Linnea[/name_f]
[name_f]Larissa[/name_f]
[name_f]Lucy[/name_f]
[name_f]Lucia[/name_f]
[name_f]Laura[/name_f]
[name_f]Lauren[/name_f]
[name_f]Laurel[/name_f]
[name_f]Maura[/name_f]
[name_f]Miranda[/name_f]
[name_f]Millicent[/name_f]
[name_u]Meredith[/name_u]
[name_f]Margo[/name_f]
[name_f]Mira[/name_f]
[name_f]Matilda[/name_f]
[name_f]Marissa[/name_f]
[name_f]Marina[/name_f]
[name_f]Nadia[/name_f]
[name_f]Natalie[/name_f]
[name_f]Noelle[/name_f]
[name_f]Natasha[/name_f]
[name_f]Opal[/name_f]
[name_f]Ophelia[/name_f]
[name_f]Ophelie[/name_f]
[name_f]Olivia[/name_f]
Olivie
[name_f]Penelope[/name_f]
[name_f]Petra[/name_f]
[name_u]Penna[/name_u]
[name_f]Persephone[/name_f]
[name_f]Priya[/name_f]
[name_f]Ramona[/name_f]
[name_f]Rosalie[/name_f]
[name_u]Rue[/name_u]
[name_f]Raina[/name_f]
[name_u]Rain[/name_u]
Risha
Rosha
[name_f]Stella[/name_f]
[name_u]Shannon[/name_u]
[name_f]Sharon[/name_f]
[name_f]Seraphina[/name_f]
[name_f]Serena[/name_f]
[name_f]Samantha[/name_f]
[name_f]Samara[/name_f]
[name_f]Sienna[/name_f]
[name_u]Sierra[/name_u]
[name_f]Sophia[/name_f]
[name_f]Tabitha[/name_f]
[name_f]Thea[/name_f]
[name_f]Terra[/name_f]
[name_u]True[/name_u]
[name_f]Violet[/name_f]
[name_f]Victoria[/name_f]
[name_f]Vittoria[/name_f]
[name_f]Vera[/name_f]
[name_f]Vanessa[/name_f]
[name_f]Veronica[/name_f]
[name_f]Willa[/name_f]
[name_f]Winnie[/name_f]
[name_f]Yvaine[/name_f]
[name_f]Yasmine[/name_f]
Ylsa
[name_f]Ysobel[/name_f]
[name_f]Zoe[/name_f]
[name_f]Zara[/name_f]
[name_f]Zosia[/name_f]
[name_f]Zinnia[/name_f]