Girls
Anna nn Annie - I like Anna but not Annie
Emma - it's ok. I find it a bit boring but I don't know why really.
Lara - love it.
Naomi - love it.
Felicity nn Flick - love Felicity but not Flick. I wouldn't shorten officially but once knew a Fizzy short for Felicity which I think is cute for a child
Celia - don't like this at all. Dated and dislike the 'seal' sound
Josephine nn Jo - quite like it. Bit retro.
Renee - don't like it. Dated again.
Boys
Samuel nn Sam - ok but seems like nearly everyone has a Sam
Charles nn Charlie - those that don't have a Sam have a Charlie? But again, quite nice.
Alexander nn Alex - I love Alexander. There are a lot of Alexs around too though.
Elliott - love it
Montgomery nn Monty - very posh but I love it
Finn - really like it. Would use Finley
Arthur - not keen. I know it's very trendy but still seems a bit old man to me.
I would choose Lara and Elliot
Second choices Naomi and Monty
Your lists are quite varied so hard to think of specifically similar choices but I would say:
Similar to Anna and Emma -
Amy, Bethany, Claire, Chloe, Charlotte, Daisy, Ella, Eva, Erin, Freya, Grace, Hannah, Isla, Isabel, Jessica, Jade, Jasmine, Katie, Lily, Lucy, Leah, Lydia, Molly, Millie, Olivia, Poppy, Phoebe, Ruby, Rosie, Rosa, Rebecca, Robyn, Sarah, Sophie, Thea, Zoe
Similar to Lara and Felicity -
Aria, Anya, Astrid, Aphra, Alexis, Bronte, Cleo, Coco, Carys, Cerys, Dana, Etta, Enya, Effie, Faith, Giselle, Greta, Hebe, Heidi, Iona, Iris, Juliet, Keziah, Livia, Larissa, Laura, Miranda, Mila, Mala, Mara, Nyah, Noa, Orla, Piper, Quinn, Rhiannon, Saffron, Sylvia, Sadie, Stella, Tessa, Tamara, Tara, Verity, Xanthe, Zara
Similar to Naomi (and Anna, I guess - two camps) -
Abigail, Adah, Dinah, Delilah, Deborah, Esther, Elizabeth, Eve Hannah, Jemima, Joanna, Julia, Keziah, Lois, Lydia, Leah, Martha, Miriam, Mary, Phoebe, Susanna, Ruth, Rebekah, Rachel, Sarah, Tamar, Tabitha, Zillah
Similar to Celia, Josephine and Renee -
Anita, April, Althea, Betty, Betsy, Connie, Cynthia, Cecilia, Denise, Daphne, Eileen, Fiona, Gwendoline, Geraldine, Helen, Irene, Julie, Jacqueline, Jocelyn, Karen, Louise, Marie, Michelle, Margot, Nina, Nadine, Pamela, Pauline, Rhona, Rhonda, Rita, Sandra, Simone, Stella, Susan, Thalia, Valerie, Violet, Vivienne, Winifred, Yolanda, Yvonne, Yvette
Similar to Samuel/Sam, Charles/Charlie and Alexander/Alex -
Benjamin/Ben, Christopher/Chris, Daniel/Dan, David/Dave, Edward/Ed, Frederick/Freddie, Henry/Harry, Jonathan/Johnny, James/Jamie, Joseph/Joe, Jacob/Jake, Matthew/Matt, Nicholas/Nick, Oliver/Oli, Thomas/Tom, William/Will, Zachary/Zach
Similar to Elliot and Finn -
Arlo, Caleb, Christian, Dylan, Ellis, Evan, Fraser, Ferdi, Gabriel, Isaac, Jesse, Jude, Logan, Milo, Nico, Nathaniel, Oscar, Patrick, Reuben, Rory, Solly, Theo
Similar to Montgomery/Monty -
Barnaby, Frederick, Ferdinand/Ferdi, George, Ptolemy, Rafferty, Raphael, Vincent, Xavier
Similar to Arthur -
Albert, Archibald, Douglas, Edwin, Eustace, Francis, Hilary, Jeremy, Jeremiah, Kenneth, Norman, Phillip, Robert, Richard, Simon, Seth, Timothy, Victor