Via, Ollie, and Livvy are popular. My favorite is Liv, especially as used by Detective Stabler while flexing and chasing perps in NYC.
Famous people named Olivia:
Gladiator Olivia Pope from Scandal; Olivia Newton-John; Olivia Benson from SVU.
This name was first used in this spelling by William Shakespeare for a character in his comedy Twelfth Night.
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