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I'm not a huge nickname person in general, but from your list I do like:
Olivia "Liv"
Abigail "Abbie"
Elizabeth "Libby"
Katherine "Kate"
Adelaide "Addy" (though I'd spell it Addie)
William "Will/Liam"
Benjamin "Ben"
James "Jamie"
Daniel "Dan"
Samuel "Sam"
Theodore "Theo"
Nathaniel "Nathan/Nate"

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I also like these but not any of the nicknames you listed:
Gabriella
Isabelle (prefer Isabel)
Rebecca
Eleanor (I do like Nell)
Amelia
Matilda
Emilia
Charlotte
Ellen
Jacob
Alexander
Joseph
Andrew
David
Michael
Henry
Jonathan
Thomas
Sophia