I'm a Rebecca and get a fairly equal dose of Rebecca, Becky and Bex peppered with a few Beccas and even the odd Rebecky, Bexsta, Reebok.
I don't like any of the nicknames but feel a bit standoffish to insist on Rebecca. I don't care all that much. And I'm always Rebecca at work.
I love Natasha, Jessica, Gabriella, Matilda, Abigail, Isabella and Madeleine but not too keen on Nat/Tash, Jess/Jessie, Gabby, Mattie/Tilly, Abbie/Gail, Izzy or Maddie. I don't hate the nicknames at all, I just think they spoil beautiful names.
I do hate Immy for Imogen, Livvy for Olivia, Clo for Chloe, Mils for Amelia, Mima/Jem for Jemima and Em/Emz for Emma/Emily