This! Pepita, Beppe, Fifi, Finka, Posey; Coos, Akiva; Hanne, Nina, Netta, Vana--they can find a J-name with a standard non-J nickname in any European language.

(If 'J' was made up for the letter and it's actually something else, it might be a little harder, but I guarantee they can find something. Traditional nicknames can be wildly removed from the base name, and a lot of them are just old-fashioned enough to sound fresh: Polly, Peg, Gretchen, Lottie, Dora, Ned, Teddy, Nancy...)