Polkadotfanatic I really feel you should be able to name your child a name you both like a lot.
I do feel your DH should be willing to compromise.
Personally, I really like the name Elisabeth and love the nick name Libby, but I do understand you may not.
I think others have said about choosing a name together. If he likes the name Elizabeth and has for years and you are happy to have it as a middle name, how about having another name first that you both agree to and making your own lists as others have suggested.
Just FYI, as I am sure you know, according to Internet Elizabeth has 152 variant forms. IF you like any of them enough, would you be happy to call her Elizabeth and use one of these names are a nickname?
variant forms: Alixyveth, Babette, Belita, Bell, Bella, Belle, Bess, Bessie, Bessy, Bet, Beta, Beth, Bethie, Betina, Betsey, Betsie, Betsy, Bett, Betta, Bette, Betti, Bettina, Bettine, Betty, Bettye, Bit, Bizzy, Buffy, Eilis, Eilish, Eleisa, Eliesse, Elisa, Elisabet, Elisabeth, Elisabethe, Elisabetta, Elisah, Elise, Elissa, Eliszabeth, Elixyveth, Eliz, Eliza, Elizabet, Elizabeth, Elizabett, Elizabette, Elizabiff, Elizabith, Elize, Elizebeth, Elle, Ellissa, Elliza, Ellsa, Ellse, Ellsee, Ellsey, Ellsi, Ellspet, Ellyse, Ellyssa, Ellyza, Elsa, Elsabeth, Else, Elsee, Elsie, Elspet, Elspeth, Elsy, Elyse, Elyssa, Elyza, Elyzza, Elzabeth, Elzbieta, Esabeau, Helsa, Ilsa, Ilse, Isabel, Isabella, Isabelle, Isobel, Leasa, Leesa, Leeza, Leisa, Leizel, Lib, Libbey, Libbi, Libbie, Libby, Libbye, Liese, Liesel, Lilibet, Lilibeth, Lisa, Lisabeth, Lisbet, Lisbeth, Lisbett, Lisbetta, Lisbette, Lise, Lisette, Lisel, Lisl, Lissa, Lissette, Lissi, Lissie, Lissy, Liz, Liza, Lizabeth, Lizbet, Lizbeth, Lizbett, Lizeth, Lizette, Lizveth, Lizy, Lizz, Lizzi, Lizzie, Lizzy, Lusa, Lysa, Lysbet, Lysbeth, Lysbette, Lyse, Lyssa, Lyssi, Lyssie, Lyza, Lyzbet, Lyzbeth, Lyzbette, Lyzette, Tetty, Veta, Ylisabet, Ylisabette, Ysabel, Ysabella and Yzabelle.
But ultimately unless you also really like the name I would try and compromise together.
Congratulations and please don't let this spoil this great time for you.