Bliss or [name_f]Beth[/name_f] would be my first choices. I also second the suggestions of giving her the same initials.
You could always use some form of [name_f]Elizabeth[/name_f] of which there are many like…
Alzbeta, Ealisaid, Eliete, [name_f]Elisa[/name_f], Eliza, [name_f]Elizabete[/name_f], Elizabeta, Elizavet, [name_f]Elle[/name_f], Elixabete, [name_f]Elspeth[/name_f], [name_f]Elzbieta[/name_f], [name_f]Ellie[/name_f], [name_f]Elzbute[/name_f], Erzsebet, [name_u]Elishua[/name_u], [name_f]Elise[/name_f], Irihapeti, [name_f]Isabella[/name_f]/Isabel, Chabela, [name_f]Liza[/name_f], Erzsi, [name_f]Isabeau[/name_f], [name_f]Ishbel[/name_f], [name_f]Lisbeth[/name_f], ’’[name_u]Sabel[/name_u]’’, [name_f]Sabela[/name_f], Ybel, [name_f]Zabel[/name_f], [name_f]Ailsa[/name_f], [name_f]Alzira[/name_f], [name_f]Effy[/name_f], Ealish, Elbie, Eliamma, Elisete, [name_f]Ella[/name_f], [name_f]Elissa[/name_f], [name_f]Elka[/name_f], [name_f]Ellen[/name_f], [name_f]Elsa[/name_f], [name_f]Elsie[/name_f], Elunia, [name_f]Elzira[/name_f], [name_f]Elzunia[/name_f], [name_f]Ilsa[/name_f], [name_u]Isa[/name_u], [name_u]Izzy[/name_u], [name_f]Lizzy[/name_f], [name_u]Lisa[/name_u], [name_f]Lela[/name_f], [name_f]Liesel[/name_f], [name_f]Lila[/name_f], [name_f]Lilli[/name_f]/Lily, Liliani, [name_f]Lilianna[/name_f], [name_f]Lisanne[/name_f], Lisen, [name_f]Liselotte[/name_f], Liset, [name_f]Lisetta[/name_f], [name_f]Zsoka[/name_f], [name_f]Babette[/name_f], [name_f]Ibbie[/name_f], Libby’’, Liddy, /Bella, [name_f]Beta[/name_f], Beth, [name_f]Bethan[/name_f], [name_f]Betsan[/name_f], Betsy, [name_f]Bette[/name_f], [name_f]Betty[/name_f], [name_u]Blair[/name_u], [name_f]Buffy[/name_f], [name_f]Etty[/name_f], [name_f]Bea[/name_f], Birdie/Bertie, Bizzy, [name_f]Lisbet[/name_f], [name_m]Elby[/name_m], Elsinue, Izabeth
And I’m sure there’s more! If none of these are your style