(WSJ) - For generations, Alen Bibic's family has been making a traditional wine known as Prosek from grapes grown in the limestone hills surrounding this small town on Croatia's Dalmatian Coast.

But this Balkan nation's entry into the European Union on July 1 has Mr. Bibic and his fellow vintners confronting an unsettling question: Will their Prosek, by any other name, taste as sweet?

When Croatia joined Europe's now 28-member common market, it was plunged into the Continent's internecine wine wars, in which countries battle to protect local producers by enforcing strict appellation rules.

Italian wine growers contend that Prosek sounds too much like Prosecco, an Italian sparkling wine.

They say that if Croatia doesn't voluntarily stop using the name, they will lodge a complaint with EU authorities to force the change.

"How would you feel if you wake up one day and you can't do something that your family has been doing for centuries?" asked the sunburned Mr. Bibic, whose amber-colored Prosek has won international awards.