Be-re-NAI-see is long and unattractive. Be-re-NEES isn't bad at all.
Bernice is not a fave; long ago in a ballet class for 8-year-olds, the incompetent teacher (who knew enough to know that French was the language of dance!) used to call a classmate BER-ne-SEE, which added to the universal torment. That
Bernice, by the way, was named "after" her
German father, Berndt or
Bernard, depending on which country he was in at the time. They were both known as
Bernie.