True enough, as I understand it from my Jewish friends, but Hebrew isn't Yiddish and it's my impression that the "Hebrew name used in the synagogue" actually has to be Hebrew - and, if possible, biblical - for instance, I know a
Jackie who was married under the name of
Yael, to a
Denis who became
David for the occasion. But he wouldn't have had two non-Hebrew names; there wouldn't be any point.
Indeed, a lot of the (South African) Jews I know have only got one given name - an English one - and then their Hebrew name can double as a middle name for religious purposes. Sometimes it translates their English name -
Ann = Chana - so it would seem odd to put it on official English-language documents, or so I've been told.